Parent Functions
The equation for the linear function is?
f(x)=x
Describe the transformation.
f(x)=x+2
Translate up 2 units
Describe the transformation.
f(x)= 2x2
Vertically expand by a factor of 2
What axis is the graph reflecting over?
f(x)=-x
both, because it's a linear function
Describe the transformation
f(x)=2(x-2)2-3
vertically expand by a factor of 2, right 2 units, down 3 units
The equation for the quadratic function is?
f(x)=x2
Describe the transformation.
f(x)= (x-2)2
Translate right 2 units
Describe the transformation.
f(x)=1/2(x2)
vertically compress by a factor of 2
What axis is the graph reflecting over?
f(x)=-(x2)
x-axis
Describe the transformation
f(x)= (2x-2)2+4
horizontally compress by a factor of 2, right 2, up 4
The equation for the cubix function is?
f(x)=x3
Describe the transformation.
f(x)= x3+5
Describe the transformation.
f(x)=(2x)2
horizontal compression by a factor of 2
What axis is the graph reflecting over?
f(x)=(-x)3
y-axis, because the negative is on the inside
Describe the transformation
f(x)= -(x2)+4
reflect across the x-axis, up 4 units
The equation for the Absolute value function is?
f(x)= |x|
Describe the transformation.
f(x)= |x-2|+3
Describe the transformation.
f(x)=(0.5x)2
horizontally expand by a factor of 2
What axis is the graph reflecting over?
f(x)=-|x|
x-axis
Describe the transformation
f(x)= |-x+2|+5
reflect across the y-axis, left 2 units, up 5
The equation for the rational function is?
f(x)= 1/x
Describe the transformation.
f(x)= 1/(x-4) +3
right 4, up 3
Describe the transformation.
f(x)=3/x
vertically expand by a factor of 3
f(x)=-1/x
reflect the rational function across the x-axis
Describe the transformation
f(x)=3/(x+3) +5
vertically expand by a factor of 3, left 3 units, up 5