Review parent functions Graph Functions
by shiftsFind domain, range,
and intercepts
Day 5
Book Section 7.8
Get 2 grids for the 2 shift problems!
Domain: Range:
Y= Absolute Value Parent Function , ),0[
x y
-2 2
-1 1
0 0
1 1
2 2
Ex. 1
Domain: Range:
y=x2 Quadratic Parent Function , ),0[
x y
-2 4
-1 1
0 0
1 1
2 4
Ex. 2
Graph y = Domain:
Range:
,0 ,0
Ex. 3 Square Root Parent Function
x y
0 0
1 1
4 2
9 3
16 4
Domain: Range:
y=x3 Cubic Parent Function
Y scale: count by twos
, ,
x y
-2 -8
-1 -1
0 0
1 1
2 8
Ex. 4
Graph y = Domain:
Range:
,
,
Ex. 5 Cube root Parent Function
x y
-8 -2
-1 -1
0 0
1 1
8 2
Domain: Range:
f(x) = 122 x
Plot the parent function and shift each point:
Shift Left 2 and up 1
),2[ ),1[
x y
0 0
1 1
4 2
9 3
16 4
Shift using parent table and multiplying y values by 2
Ex. 6
Domain: Range:
f(x)= 462 3 x
Plot the parent function and shift each point:
Left 6 and down 4
),[ ),[
x y
-8 -2
-1 -1
0 0
1 1
8 2
Shift using parent table and multiplying y values by 2
Ex. 7
Shift coordinate:
Domain:
Range:
y-intercept:
x-intercept:
43)( 2 xxf
(3,-4)
(-∞,∞)
[-4,∞)
(0,5)
(5,0)
y=(0-3)2 – 4 y=(-3)2 – 4 y=5
0=(x-3)2 – 4
4=(x-3)2
4=x2-6x+90=x2-6x+50=(x-5)(x-1)
(1,0)
Ex. 8
Shift coordinate:
Domain:
Range:
y-intercept:
x-intercept:
482)( xxf
(-4,-4)
(-∞,∞)
[-4,∞)
(0,4)
(-2,0)
Y= – 4
y=40= – 4
4 =
2x+8 = 4 or 2x+8 = -4
x = -2 or x = -6
(-6,0)
802
Y= – 4 8
82 x
82 x
Ex. 9
Shift coordinate:
Domain:
Range:
y-intercept:
x-intercept:
12)( 3 xxf
(2,1)
(-∞,∞)
(-∞,∞)
(0,-7)
(1,0)
y=(0-2)3 + 1 y=(-2)3 + 1 y= -7
0=(x-2)3 + 1
-1=(x-2)3
Take cube root of both sides-1 = x – 2
x = 1
Ex. 10
Shift coordinate:
Domain:
Range:
y-intercept:
x-intercept:
(1,2)
(-∞,∞)
(-∞,∞)
(0,1)
(-7,0)
21)( 3 xxfEx. 11