11 x1 t02 07 sketching graphs (2012)
TRANSCRIPT
Sketching Graphs
Sketching Graphs* Numbers on axes must be evenly spaced
Sketching Graphs* Numbers on axes must be evenly spaced
* y intercept occurs when x = 0
Sketching Graphs* Numbers on axes must be evenly spaced
* y intercept occurs when x = 0
* x intercept occurs when y = 0
Sketching Graphs* Numbers on axes must be evenly spaced
* y intercept occurs when x = 0
* x intercept occurs when y = 0
Once the intercepts have been found, curves are easy to sketch, if you know the basic shape.
Sketching Graphs* Numbers on axes must be evenly spaced
* y intercept occurs when x = 0
* x intercept occurs when y = 0
Once the intercepts have been found, curves are easy to sketch, if you know the basic shape.
If in doubt use a table of values and plot some points
Basic Curves
Basic Curvesxy
(1) Straight Linesy
x
Basic Curves
bmxy
xy (1) Straight Lines
y
x
Basic Curves
bmxy
xy 1̀power
(1) Straight Linesy
x 1̀power
Basic Curves
bmxy
xy 1̀power
(1) Straight Linesy
x 1̀power
(2) Parabolay
x
2xy
Basic Curves
bmxy
xy
cbxaxy 2
1̀power
(1) Straight Linesy
x 1̀power
(2) Parabolay
x
2xy
Basic Curves
bmxy
xy
cbxaxy 2
1̀power
(1) Straight Linesy
x 1̀power
(2) Parabolay
x
2xy 1̀power
2̀power
Basic Curves
bmxy
xy
cbxaxy 2
1̀power
0solve 2 cbxax
(1) Straight Linesy
x 1̀power
(2) Parabolay
x
2xy 1̀power
2̀power x intercepts:
Basic Curves
bmxy
xy
cbxaxy 2
1̀power
0solve 2 cbxax
(1) Straight Linesy
x 1̀power
(2) Parabolay
x
2xy 1̀power
2̀power x intercepts:
vertex: halfway between x intercepts
e.g. find the x intercepts and vertex of 342 xxy
e.g. find the x intercepts and vertex of 342 xxy 12 2 xy
1,2vertex
e.g. find the x intercepts and vertex of 342 xxy 12 2 xy
1,2vertex 12 2 xx intercepts:
e.g. find the x intercepts and vertex of 342 xxy 12 2 xy
1,2vertex 12 2 xx intercepts:
1212
x
x
x = 1 or x = 3
e.g. find the x intercepts and vertex of 342 xxy 12 2 xy
1,2vertex 12 2 xx intercepts:
1212
x
x
x = 1 or x = 3y
x1 1,2
3
e.g. find the x intercepts and vertex of 342 xxy 12 2 xy
1,2vertex 12 2 xx intercepts:
1212
x
x
x = 1 or x = 3y
x1 1,2
3
(3) Cubic
y
x
3xy
e.g. find the x intercepts and vertex of 342 xxy 12 2 xy
1,2vertex 12 2 xx intercepts:
1212
x
x
x = 1 or x = 3y
x1 1,2
3
(3) Cubic
y
x
3xy dcxbxaxy 23
e.g. find the x intercepts and vertex of 342 xxy 12 2 xy
1,2vertex 12 2 xx intercepts:
1212
x
x
x = 1 or x = 3y
x1 1,2
3
(3) Cubic
y
x
3xy dcxbxaxy 23
1̀power
3̀power
e.g. find the x intercepts and vertex of 342 xxy 12 2 xy
1,2vertex 12 2 xx intercepts:
1212
x
x
x = 1 or x = 3y
x1 1,2
3
(3) Cubic
y
x
3xy dcxbxaxy 23
1̀power
3̀power
cubic.basicthelikelook it willthen
tofactorised becan it If 3kxay
e.g. find the x intercepts and vertex of 342 xxy 12 2 xy
1,2vertex 12 2 xx intercepts:
1212
x
x
x = 1 or x = 3y
x1 1,2
3
(3) Cubic
y
x
3xy dcxbxaxy 23
1̀power
3̀power
cubic.basicthelikelook it willthen
tofactorised becan it If 3kxay
Otherwise;y
x
(4) Higher Powersy
x
etc
even
6
4
xy
xy
(4) Higher Powersy
x
etc
even
6
4
xy
xy
y
x
etc
odd
7
5
xy
xy
(4) Higher Powersy
x
etc
even
6
4
xy
xy
y
x
etc
odd
7
5
xy
xy
As power gets bigger, curve gets; - flatter at base- steeper at the sides
(4) Higher Powersy
x
etc
even
6
4
xy
xy
y
x
etc
odd
7
5
xy
xy
As power gets bigger, curve gets; - flatter at base- steeper at the sides
(5) Hyperbolay
x
(4) Higher Powersy
x
etc
even
6
4
xy
xy
y
x
etc
odd
7
5
xy
xy
As power gets bigger, curve gets; - flatter at base- steeper at the sides
(5) Hyperbolay
x 1
1
xyOR
xy
(4) Higher Powersy
x
etc
even
6
4
xy
xy
y
x
etc
odd
7
5
xy
xy
As power gets bigger, curve gets; - flatter at base- steeper at the sides
(5) Hyperbolay
x 1
1
xyOR
xy
xy 1
one power on top of a fraction, one power on bottom of fraction
(6) Circley
x
222 ryx
r
r
-r
-r
(6) Circley
x
222 ryx 222 ryx
r
r
-r
-rboth power ‘2’coefficients are the same
(6) Circley
x
222 ryx
y
x
1
aay x
(7) Exponential
222 ryx
r
r
-r
-rboth power ‘2’coefficients are the same
1
(6) Circley
x
222 ryx
y
x
1
aay x
(7) Exponential
222 ryx
r
r
-r
-rboth power ‘2’coefficients are the same
xay
pronumeral in the power
1
(8) Rootsy
x
22 xry
r
r
-r
(8) Rootsy
x
22 xry y
x
xy
r
r
-r
(8) Rootsy
x
22 xry y
x
xy
r
r
-r
to tell what the curve looks like, square both sides
(8) Rootsy
x
22 xry y
x
xy
r
r
-r
to tell what the curve looks like, square both sides
circle
222
222
22
ryxxryxry
(8) Rootsy
x
22 xry y
x
xy
r
r
-r
to tell what the curve looks like, square both sides
circle
222
222
22
ryxxryxry
parabola
2
xyxy
(8) Rootsy
x
22 xry y
x
xy
r
r
-r
to tell what the curve looks like, square both sides
circle
222
222
22
ryxxryxry
parabola
2
xyxy
half topmeans
halfbottommeans
(8) Rootsy
x
22 xry y
x
xy
r
r
-r
to tell what the curve looks like, square both sides
circle
222
222
22
ryxxryxry
parabola
2
xyxy
half topmeans
halfbottommeans Exercise 2G; 1adeh, 2adgk, 3bdf, 5aeh, 7acegi, 8ad, 9a, 11c, 13acd,
15bd, 17*