10/13/2015mrs. liu's precalc day191 cp calculus block 19 hw-review p88, 84;90;96;108;114;...
TRANSCRIPT
![Page 1: 10/13/2015Mrs. Liu's PreCalc Day191 CP Calculus Block 19 HW-Review p88, 84;90;96;108;114; 120;126;](https://reader031.vdocuments.site/reader031/viewer/2022032606/56649eb25503460f94bb90c9/html5/thumbnails/1.jpg)
04/19/23 Mrs. Liu's PreCalc Day19 1
CP Calculus Block 19 HW-Review p88,
84;90;96;108;114; 120;126;
![Page 2: 10/13/2015Mrs. Liu's PreCalc Day191 CP Calculus Block 19 HW-Review p88, 84;90;96;108;114; 120;126;](https://reader031.vdocuments.site/reader031/viewer/2022032606/56649eb25503460f94bb90c9/html5/thumbnails/2.jpg)
04/19/23 Mrs. Liu's PreCalc Day19 2
CP Calculus Block 19
HW p98,x3’s
3-48
![Page 3: 10/13/2015Mrs. Liu's PreCalc Day191 CP Calculus Block 19 HW-Review p88, 84;90;96;108;114; 120;126;](https://reader031.vdocuments.site/reader031/viewer/2022032606/56649eb25503460f94bb90c9/html5/thumbnails/3.jpg)
04/19/23 Mrs. Liu's PreCalc Day19 3
Ch 2.4 Continuity and One-sided Limit
![Page 4: 10/13/2015Mrs. Liu's PreCalc Day191 CP Calculus Block 19 HW-Review p88, 84;90;96;108;114; 120;126;](https://reader031.vdocuments.site/reader031/viewer/2022032606/56649eb25503460f94bb90c9/html5/thumbnails/4.jpg)
04/19/23 Mrs. Liu's PreCalc Day19 4
Do Now:
2
x 2, x 0
f (1
, x
xx0
) 1
x
![Page 5: 10/13/2015Mrs. Liu's PreCalc Day191 CP Calculus Block 19 HW-Review p88, 84;90;96;108;114; 120;126;](https://reader031.vdocuments.site/reader031/viewer/2022032606/56649eb25503460f94bb90c9/html5/thumbnails/5.jpg)
04/19/23 Mrs. Liu's PreCalc Day19 5
2
1x
x 2 11
x 1 x 1
2
![Page 6: 10/13/2015Mrs. Liu's PreCalc Day191 CP Calculus Block 19 HW-Review p88, 84;90;96;108;114; 120;126;](https://reader031.vdocuments.site/reader031/viewer/2022032606/56649eb25503460f94bb90c9/html5/thumbnails/6.jpg)
04/19/23 Mrs. Liu's PreCalc Day19 6
2
xlim f ( x )
0
![Page 7: 10/13/2015Mrs. Liu's PreCalc Day191 CP Calculus Block 19 HW-Review p88, 84;90;96;108;114; 120;126;](https://reader031.vdocuments.site/reader031/viewer/2022032606/56649eb25503460f94bb90c9/html5/thumbnails/7.jpg)
04/19/23 Mrs. Liu's PreCalc Day19 7
2
xlim f ( x )
1
![Page 8: 10/13/2015Mrs. Liu's PreCalc Day191 CP Calculus Block 19 HW-Review p88, 84;90;96;108;114; 120;126;](https://reader031.vdocuments.site/reader031/viewer/2022032606/56649eb25503460f94bb90c9/html5/thumbnails/8.jpg)
04/19/23 Mrs. Liu's PreCalc Day19 8
2x 0lim f ( x )
![Page 9: 10/13/2015Mrs. Liu's PreCalc Day191 CP Calculus Block 19 HW-Review p88, 84;90;96;108;114; 120;126;](https://reader031.vdocuments.site/reader031/viewer/2022032606/56649eb25503460f94bb90c9/html5/thumbnails/9.jpg)
04/19/23 Mrs. Liu's PreCalc Day19 9
2x 0lim f ( x )
2
![Page 10: 10/13/2015Mrs. Liu's PreCalc Day191 CP Calculus Block 19 HW-Review p88, 84;90;96;108;114; 120;126;](https://reader031.vdocuments.site/reader031/viewer/2022032606/56649eb25503460f94bb90c9/html5/thumbnails/10.jpg)
04/19/23 Mrs. Liu's PreCalc Day19 10
Objective 1: Determine the
continuity of the functions
![Page 11: 10/13/2015Mrs. Liu's PreCalc Day191 CP Calculus Block 19 HW-Review p88, 84;90;96;108;114; 120;126;](https://reader031.vdocuments.site/reader031/viewer/2022032606/56649eb25503460f94bb90c9/html5/thumbnails/11.jpg)
04/19/23 Mrs. Liu's PreCalc Day19 11
Definition A: Continuity at an interior point
x clim f(x) = f(c)
![Page 12: 10/13/2015Mrs. Liu's PreCalc Day191 CP Calculus Block 19 HW-Review p88, 84;90;96;108;114; 120;126;](https://reader031.vdocuments.site/reader031/viewer/2022032606/56649eb25503460f94bb90c9/html5/thumbnails/12.jpg)
04/19/23 Mrs. Liu's PreCalc Day19 12
Definition B: Continuity on closed interval [a,b], left endpoint a or right endpoint b
![Page 13: 10/13/2015Mrs. Liu's PreCalc Day191 CP Calculus Block 19 HW-Review p88, 84;90;96;108;114; 120;126;](https://reader031.vdocuments.site/reader031/viewer/2022032606/56649eb25503460f94bb90c9/html5/thumbnails/13.jpg)
04/19/23 Mrs. Liu's PreCalc Day19 13
b
+
-
x a
x
lim f(x) = f( )
lim f(x)
a
= f(b)
![Page 14: 10/13/2015Mrs. Liu's PreCalc Day191 CP Calculus Block 19 HW-Review p88, 84;90;96;108;114; 120;126;](https://reader031.vdocuments.site/reader031/viewer/2022032606/56649eb25503460f94bb90c9/html5/thumbnails/14.jpg)
04/19/23 Mrs. Liu's PreCalc Day19 14
Definition C: A function is continuous if it is continuous at each point of its domain
![Page 15: 10/13/2015Mrs. Liu's PreCalc Day191 CP Calculus Block 19 HW-Review p88, 84;90;96;108;114; 120;126;](https://reader031.vdocuments.site/reader031/viewer/2022032606/56649eb25503460f94bb90c9/html5/thumbnails/15.jpg)
04/19/23 Mrs. Liu's PreCalc Day19 15
The Continuity Test The function y=f(x) is continuous at x=c if and only if all of the following are true:
![Page 16: 10/13/2015Mrs. Liu's PreCalc Day191 CP Calculus Block 19 HW-Review p88, 84;90;96;108;114; 120;126;](https://reader031.vdocuments.site/reader031/viewer/2022032606/56649eb25503460f94bb90c9/html5/thumbnails/16.jpg)
04/19/23 Mrs. Liu's PreCalc Day19 16
x c
x c
ii ) limf(x) exists
iii) li
i
m
) f(c) ex
f(x
itst
) = c)
s
f(
![Page 17: 10/13/2015Mrs. Liu's PreCalc Day191 CP Calculus Block 19 HW-Review p88, 84;90;96;108;114; 120;126;](https://reader031.vdocuments.site/reader031/viewer/2022032606/56649eb25503460f94bb90c9/html5/thumbnails/17.jpg)
04/19/23 Mrs. Liu's PreCalc Day19 17
Existence of Limit
cx x clim f ( x ) lim f
L
( x )
![Page 18: 10/13/2015Mrs. Liu's PreCalc Day191 CP Calculus Block 19 HW-Review p88, 84;90;96;108;114; 120;126;](https://reader031.vdocuments.site/reader031/viewer/2022032606/56649eb25503460f94bb90c9/html5/thumbnails/18.jpg)
04/19/23 Mrs. Liu's PreCalc Day19 18
Properties of Continuity I Scalar Multiple: bf(x)
![Page 19: 10/13/2015Mrs. Liu's PreCalc Day191 CP Calculus Block 19 HW-Review p88, 84;90;96;108;114; 120;126;](https://reader031.vdocuments.site/reader031/viewer/2022032606/56649eb25503460f94bb90c9/html5/thumbnails/19.jpg)
04/19/23 Mrs. Liu's PreCalc Day19 19
Properties of Continuity ii Sum or difference f + g, or f - g
![Page 20: 10/13/2015Mrs. Liu's PreCalc Day191 CP Calculus Block 19 HW-Review p88, 84;90;96;108;114; 120;126;](https://reader031.vdocuments.site/reader031/viewer/2022032606/56649eb25503460f94bb90c9/html5/thumbnails/20.jpg)
04/19/23 Mrs. Liu's PreCalc Day19 20
Properties of Continuity iii Product f(x)g(x)
![Page 21: 10/13/2015Mrs. Liu's PreCalc Day191 CP Calculus Block 19 HW-Review p88, 84;90;96;108;114; 120;126;](https://reader031.vdocuments.site/reader031/viewer/2022032606/56649eb25503460f94bb90c9/html5/thumbnails/21.jpg)
04/19/23 Mrs. Liu's PreCalc Day19 21
Properties of Continuity iv Quotient f(x)/g(x)g( x ) 0
![Page 22: 10/13/2015Mrs. Liu's PreCalc Day191 CP Calculus Block 19 HW-Review p88, 84;90;96;108;114; 120;126;](https://reader031.vdocuments.site/reader031/viewer/2022032606/56649eb25503460f94bb90c9/html5/thumbnails/22.jpg)
04/19/23 Mrs. Liu's PreCalc Day19 22
Continuity of Composite Functions f(g(x)) or g(f(x))
![Page 23: 10/13/2015Mrs. Liu's PreCalc Day191 CP Calculus Block 19 HW-Review p88, 84;90;96;108;114; 120;126;](https://reader031.vdocuments.site/reader031/viewer/2022032606/56649eb25503460f94bb90c9/html5/thumbnails/23.jpg)
04/19/23 Mrs. Liu's PreCalc Day19 23
Theorem: If f is continuous at c and g is continuous at f©, then the composite gof is continuous at c.
![Page 24: 10/13/2015Mrs. Liu's PreCalc Day191 CP Calculus Block 19 HW-Review p88, 84;90;96;108;114; 120;126;](https://reader031.vdocuments.site/reader031/viewer/2022032606/56649eb25503460f94bb90c9/html5/thumbnails/24.jpg)
04/19/23 Mrs. Liu's PreCalc Day19 24
Example 0 Given f(x)
21 x , 0 x
x
1,
f ( x
,
)
x
1 x 1
0
1
![Page 25: 10/13/2015Mrs. Liu's PreCalc Day191 CP Calculus Block 19 HW-Review p88, 84;90;96;108;114; 120;126;](https://reader031.vdocuments.site/reader031/viewer/2022032606/56649eb25503460f94bb90c9/html5/thumbnails/25.jpg)
04/19/23 Mrs. Liu's PreCalc Day19 25
21 x , 0 x
x
1,
f ( x
,
)
x
1 x 1
0
1
a) Determine a complete graph of f(x)
![Page 26: 10/13/2015Mrs. Liu's PreCalc Day191 CP Calculus Block 19 HW-Review p88, 84;90;96;108;114; 120;126;](https://reader031.vdocuments.site/reader031/viewer/2022032606/56649eb25503460f94bb90c9/html5/thumbnails/26.jpg)
04/19/23 Mrs. Liu's PreCalc Day19 26
21 x , 0 x
x
1,
f ( x
,
)
x
1 x 1
0
1
b) Is f(x) continuous? Explain.
Yes. At all points
![Page 27: 10/13/2015Mrs. Liu's PreCalc Day191 CP Calculus Block 19 HW-Review p88, 84;90;96;108;114; 120;126;](https://reader031.vdocuments.site/reader031/viewer/2022032606/56649eb25503460f94bb90c9/html5/thumbnails/27.jpg)
04/19/23 Mrs. Liu's PreCalc Day19 27
Example 1 Find the points at which the function is not continuous
2
1f ( x )
( x 2 )
x 2
![Page 28: 10/13/2015Mrs. Liu's PreCalc Day191 CP Calculus Block 19 HW-Review p88, 84;90;96;108;114; 120;126;](https://reader031.vdocuments.site/reader031/viewer/2022032606/56649eb25503460f94bb90c9/html5/thumbnails/28.jpg)
04/19/23 Mrs. Liu's PreCalc Day19 28
Example 2 Find the points at which the function is not continuous
2
x 3f ( x )
x 3x 10
x 2,5
![Page 29: 10/13/2015Mrs. Liu's PreCalc Day191 CP Calculus Block 19 HW-Review p88, 84;90;96;108;114; 120;126;](https://reader031.vdocuments.site/reader031/viewer/2022032606/56649eb25503460f94bb90c9/html5/thumbnails/29.jpg)
04/19/23 Mrs. Liu's PreCalc Day19 29
Example 3 Find the points at which the function is not continuous 2
1f ( x )
x 1
No discontinuities
![Page 30: 10/13/2015Mrs. Liu's PreCalc Day191 CP Calculus Block 19 HW-Review p88, 84;90;96;108;114; 120;126;](https://reader031.vdocuments.site/reader031/viewer/2022032606/56649eb25503460f94bb90c9/html5/thumbnails/30.jpg)
04/19/23 Mrs. Liu's PreCalc Day19 30
Example 4 Find the points at which the function is not continuous
No discontinuities
f ( x ) 2x 3
![Page 31: 10/13/2015Mrs. Liu's PreCalc Day191 CP Calculus Block 19 HW-Review p88, 84;90;96;108;114; 120;126;](https://reader031.vdocuments.site/reader031/viewer/2022032606/56649eb25503460f94bb90c9/html5/thumbnails/31.jpg)
04/19/23 Mrs. Liu's PreCalc Day19 31
Example 5 Find the points at which the function is not continuous
x=0
xf ( x )
x
![Page 32: 10/13/2015Mrs. Liu's PreCalc Day191 CP Calculus Block 19 HW-Review p88, 84;90;96;108;114; 120;126;](https://reader031.vdocuments.site/reader031/viewer/2022032606/56649eb25503460f94bb90c9/html5/thumbnails/32.jpg)
04/19/23 Mrs. Liu's PreCalc Day19 32
Example 6 Find the points at which the function is not continuous
4f ( x ) 3x 1 x<1/3
![Page 33: 10/13/2015Mrs. Liu's PreCalc Day191 CP Calculus Block 19 HW-Review p88, 84;90;96;108;114; 120;126;](https://reader031.vdocuments.site/reader031/viewer/2022032606/56649eb25503460f94bb90c9/html5/thumbnails/33.jpg)
04/19/23 Mrs. Liu's PreCalc Day19 33
Example 7 Find the points at which the function is not continuousNo discontinuities
5f ( x ) 2 x
![Page 34: 10/13/2015Mrs. Liu's PreCalc Day191 CP Calculus Block 19 HW-Review p88, 84;90;96;108;114; 120;126;](https://reader031.vdocuments.site/reader031/viewer/2022032606/56649eb25503460f94bb90c9/html5/thumbnails/34.jpg)
04/19/23 Mrs. Liu's PreCalc Day19 34
Example 8 Define g(x) so that g(x)=(x2-9)/(x-3) is continuous at x=3
g(3)=6
![Page 35: 10/13/2015Mrs. Liu's PreCalc Day191 CP Calculus Block 19 HW-Review p88, 84;90;96;108;114; 120;126;](https://reader031.vdocuments.site/reader031/viewer/2022032606/56649eb25503460f94bb90c9/html5/thumbnails/35.jpg)
04/19/23 Mrs. Liu's PreCalc Day19 35
Example 9 Define f(1) so that f(x)=(x3-1)/(x2-1) is continuous at x=1
3f (1)
2
![Page 36: 10/13/2015Mrs. Liu's PreCalc Day191 CP Calculus Block 19 HW-Review p88, 84;90;96;108;114; 120;126;](https://reader031.vdocuments.site/reader031/viewer/2022032606/56649eb25503460f94bb90c9/html5/thumbnails/36.jpg)
04/19/23 Mrs. Liu's PreCalc Day19 36
Example 10 Given g(x)
3
2
g( x )1
bx
1x
,
, x
2
2
x
![Page 37: 10/13/2015Mrs. Liu's PreCalc Day191 CP Calculus Block 19 HW-Review p88, 84;90;96;108;114; 120;126;](https://reader031.vdocuments.site/reader031/viewer/2022032606/56649eb25503460f94bb90c9/html5/thumbnails/37.jpg)
04/19/23 Mrs. Liu's PreCalc Day19 37
What value should be assigned to b to make g(x) continuous at x=1/2?
1b
2
![Page 38: 10/13/2015Mrs. Liu's PreCalc Day191 CP Calculus Block 19 HW-Review p88, 84;90;96;108;114; 120;126;](https://reader031.vdocuments.site/reader031/viewer/2022032606/56649eb25503460f94bb90c9/html5/thumbnails/38.jpg)
04/19/23 Mrs. Liu's PreCalc Day19 38
Example 11: Find the limit
x 0limtan x
0
![Page 39: 10/13/2015Mrs. Liu's PreCalc Day191 CP Calculus Block 19 HW-Review p88, 84;90;96;108;114; 120;126;](https://reader031.vdocuments.site/reader031/viewer/2022032606/56649eb25503460f94bb90c9/html5/thumbnails/39.jpg)
04/19/23 Mrs. Liu's PreCalc Day19 39
Example 12: Find the limit
x 0lim sin( cos(tan x ))
2
1
![Page 40: 10/13/2015Mrs. Liu's PreCalc Day191 CP Calculus Block 19 HW-Review p88, 84;90;96;108;114; 120;126;](https://reader031.vdocuments.site/reader031/viewer/2022032606/56649eb25503460f94bb90c9/html5/thumbnails/40.jpg)
04/19/23 Mrs. Liu's PreCalc Day19 40
Example 13:Example 13: Find the Find the vertical asymptote(s) ofvertical asymptote(s) of
3f(x) =
(x + 2)
![Page 41: 10/13/2015Mrs. Liu's PreCalc Day191 CP Calculus Block 19 HW-Review p88, 84;90;96;108;114; 120;126;](https://reader031.vdocuments.site/reader031/viewer/2022032606/56649eb25503460f94bb90c9/html5/thumbnails/41.jpg)
04/19/23 Mrs. Liu's PreCalc Day19 41
Example 14:Example 14: Find Find the vertical the vertical asymptote(s) ofasymptote(s) of
2
1f(x) =
x - x - 2
![Page 42: 10/13/2015Mrs. Liu's PreCalc Day191 CP Calculus Block 19 HW-Review p88, 84;90;96;108;114; 120;126;](https://reader031.vdocuments.site/reader031/viewer/2022032606/56649eb25503460f94bb90c9/html5/thumbnails/42.jpg)
04/19/23 Mrs. Liu's PreCalc Day19 42
2
1f(x) =
x - x - 21
=(x + 1)(x - 2)
x = 2
x = -1
![Page 43: 10/13/2015Mrs. Liu's PreCalc Day191 CP Calculus Block 19 HW-Review p88, 84;90;96;108;114; 120;126;](https://reader031.vdocuments.site/reader031/viewer/2022032606/56649eb25503460f94bb90c9/html5/thumbnails/43.jpg)
04/19/23 Mrs. Liu's PreCalc Day19 43
Example 15:Example 15: Find the Find the end behavior end behavior asymptote(s) ofasymptote(s) of
2
x + 1f(x) =
x - x - 6
![Page 44: 10/13/2015Mrs. Liu's PreCalc Day191 CP Calculus Block 19 HW-Review p88, 84;90;96;108;114; 120;126;](https://reader031.vdocuments.site/reader031/viewer/2022032606/56649eb25503460f94bb90c9/html5/thumbnails/44.jpg)
04/19/23 Mrs. Liu's PreCalc Day19 44
vertical asymptotes
end behavior asymptote (horizontal)
![Page 45: 10/13/2015Mrs. Liu's PreCalc Day191 CP Calculus Block 19 HW-Review p88, 84;90;96;108;114; 120;126;](https://reader031.vdocuments.site/reader031/viewer/2022032606/56649eb25503460f94bb90c9/html5/thumbnails/45.jpg)
04/19/23 Mrs. Liu's PreCalc Day19 45
Example 16
3
2
x
3
Find limf(x) if
2x 7f
(x) =x 7
x x
a )2
b )2
![Page 46: 10/13/2015Mrs. Liu's PreCalc Day191 CP Calculus Block 19 HW-Review p88, 84;90;96;108;114; 120;126;](https://reader031.vdocuments.site/reader031/viewer/2022032606/56649eb25503460f94bb90c9/html5/thumbnails/46.jpg)
04/19/23 Mrs. Liu's PreCalc Day19 46
Example 17
2
xFind limf(x) if
3x 7f(x)
=x 2
a )0
b )0
![Page 47: 10/13/2015Mrs. Liu's PreCalc Day191 CP Calculus Block 19 HW-Review p88, 84;90;96;108;114; 120;126;](https://reader031.vdocuments.site/reader031/viewer/2022032606/56649eb25503460f94bb90c9/html5/thumbnails/47.jpg)
04/19/23 Mrs. Liu's PreCalc Day19 47
Example 18
4
3
xFind limf(x) i
xf(x) =
f
x 1
a )
b )
![Page 48: 10/13/2015Mrs. Liu's PreCalc Day191 CP Calculus Block 19 HW-Review p88, 84;90;96;108;114; 120;126;](https://reader031.vdocuments.site/reader031/viewer/2022032606/56649eb25503460f94bb90c9/html5/thumbnails/48.jpg)
04/19/23 Mrs. Liu's PreCalc Day19 48
Example 19
5
6
x
4
Find limf(x) if
10x
x 31x
f(x) =
a )0
b )0
![Page 49: 10/13/2015Mrs. Liu's PreCalc Day191 CP Calculus Block 19 HW-Review p88, 84;90;96;108;114; 120;126;](https://reader031.vdocuments.site/reader031/viewer/2022032606/56649eb25503460f94bb90c9/html5/thumbnails/49.jpg)
04/19/23 Mrs. Liu's PreCalc Day19 49
Example 20
4
4 3 2
xFind limf(x) if
xf(x) =
x 7 x 7 x 9
a )
1
1
b )
![Page 50: 10/13/2015Mrs. Liu's PreCalc Day191 CP Calculus Block 19 HW-Review p88, 84;90;96;108;114; 120;126;](https://reader031.vdocuments.site/reader031/viewer/2022032606/56649eb25503460f94bb90c9/html5/thumbnails/50.jpg)
04/19/23 Mrs. Liu's PreCalc Day19 50
Lesson quiz 1: Given
2x 1, 1 x 0
2x , 0 x 1
f ( x ) 1, x 1
2x 4, 1 x 2
0, 2 x 3
![Page 51: 10/13/2015Mrs. Liu's PreCalc Day191 CP Calculus Block 19 HW-Review p88, 84;90;96;108;114; 120;126;](https://reader031.vdocuments.site/reader031/viewer/2022032606/56649eb25503460f94bb90c9/html5/thumbnails/51.jpg)
04/19/23 Mrs. Liu's PreCalc Day19 51
2x 1, 1 x 0
2x , 0 x 1
f ( x ) 1, x 1
2x 4, 1 x 2
0, 2 x 3
a) Does f(1) exist?yes,f (1) 1
![Page 52: 10/13/2015Mrs. Liu's PreCalc Day191 CP Calculus Block 19 HW-Review p88, 84;90;96;108;114; 120;126;](https://reader031.vdocuments.site/reader031/viewer/2022032606/56649eb25503460f94bb90c9/html5/thumbnails/52.jpg)
04/19/23 Mrs. Liu's PreCalc Day19 52
2x 1, 1 x 0
2x , 0 x 1
f ( x ) 1, x 1
2x 4, 1 x 2
0, 2 x 3
x 1b) lim f(x) exist?
x 1yes,limf ( x ) 2
![Page 53: 10/13/2015Mrs. Liu's PreCalc Day191 CP Calculus Block 19 HW-Review p88, 84;90;96;108;114; 120;126;](https://reader031.vdocuments.site/reader031/viewer/2022032606/56649eb25503460f94bb90c9/html5/thumbnails/53.jpg)
04/19/23 Mrs. Liu's PreCalc Day19 53
2x 1, 1 x 0
2x , 0 x 1
f ( x ) 1, x 1
2x 4, 1 x 2
0, 2 x 3
x 1c) Does lim f(x) = f(1)?
No
![Page 54: 10/13/2015Mrs. Liu's PreCalc Day191 CP Calculus Block 19 HW-Review p88, 84;90;96;108;114; 120;126;](https://reader031.vdocuments.site/reader031/viewer/2022032606/56649eb25503460f94bb90c9/html5/thumbnails/54.jpg)
04/19/23 Mrs. Liu's PreCalc Day19 54
2x 1, 1 x 0
2x , 0 x 1
f ( x ) 1, x 1
2x 4, 1 x 2
0, 2 x 3
d) Is f(x) continuous at x = 1?
No
![Page 55: 10/13/2015Mrs. Liu's PreCalc Day191 CP Calculus Block 19 HW-Review p88, 84;90;96;108;114; 120;126;](https://reader031.vdocuments.site/reader031/viewer/2022032606/56649eb25503460f94bb90c9/html5/thumbnails/55.jpg)
04/19/23 Mrs. Liu's PreCalc Day19 55
2x 1, 1 x 0
2x , 0 x 1
f ( x ) 1, x 1
2x 4, 1 x 2
0, 2 x 3e) At what values of x
is f(x) continuous? all points in [-1, 3]
except x = 0, 1, 2
![Page 56: 10/13/2015Mrs. Liu's PreCalc Day191 CP Calculus Block 19 HW-Review p88, 84;90;96;108;114; 120;126;](https://reader031.vdocuments.site/reader031/viewer/2022032606/56649eb25503460f94bb90c9/html5/thumbnails/56.jpg)
04/19/23 Mrs. Liu's PreCalc Day19 56
2x 1, 1 x 0
2x , 0 x 1
f ( x ) 1, x 1
2x 4, 1 x 2
0, 2 x 3f) How should h be
defined to make h a
continuous extension
of f to the point x = 1?
h( x ) f ( x )
x 1,h(1) 2