Impacts of Transformations
What impact does a have on the function f(x)=a(x+c)+d.
Stretches or shrinks the graph
The function g(x) is made by transforming the function f(x)=4x^2+1 vertically up by 3 units.
What is g(x)=4x^2+4
The function g(x) is made by transforming the function f(x)=-2^(x-1)+2 vertically down by 6 units.
What is g(x)=-2^(x-1)-4
The function g(x) is made by transforming the function f(x)=|x| vertically up by 5 units.
What is g(x)=|x|+5
Write an equation for the following transformation:
Absolute value function shifted down 2 and left 5
y=|x+5|-2
What impact does c have on the function f(x)=a(x+c)+d.
Horizontal Shift
The function g(x) is made by transforming the function f(x)=3x^2+2x-1 vertically up by 3 units.
f(x)=3x^2+2x+2
The function g(x) is made by transforming the function f(x)=2^(x+1) horizontally left by 3 units.
What is g(x)=2^(x+4)
The transformation g(x) is created by transforming the parent function of an absolute value function horizontally right by 6 units.
What is g(x)=|x-6|
Write an equation for the following transformation.
Quadratic function flipped over the x-axis, shifted right 1, and shifted up 5.
-(x-1)^2+5
What impact does d have on the function f(x)=a(x+c)+d.
Vertical Shift
The function g(x) is made by transforming the function f(x)=-2x^2+3 horizontally by 4 units to the right.
What is g(x)=-2(x-4)^2+3
The function g(x) is made by stretching the function f(x)=3^(x+9) by a factor of 4.
What is g(x)=(4)3^(x+9)
Describe the transformation of f(x)=.5|x|+1 is created by transforming the parent function.
Shift up one unit and shrink by a factor of .5
Write an equation for the following transformation.
Exponential function (2^x) shifted right 4, up 2, left 3, and down 7
2^(x-1)-5
If c is negative, what direction will the function move? f(x)=a(x+c)+d
right
This function, g(x), is created by flipping the function f(x)=2x^2 +4 over the x-axis.
What is g(x)=-2x^2+4
The function g(x) is made by transforming the function f(x)=6^(x+8) by flipping it over the x-axis and shifting it down by 3 units
What is g(x)=-6^(x+8)-3
What is the horizontal shift in the function f(x)=-2|x+4|-4
Left 4
Write an equation for the following transformation.
Absolute value function shifted up 5, down 8, right 4, left 20.
|x+16|-3
If a is negative, what will happen to the function? f(x)=a(x+c)+d
Flip over x-axis
Write an equation for the following transformation:
A quadratic function shifted down 3 units and right 1 unit.
f(x)=(x-1)^2-3
How does f(x)=2^(x-3)+3 change to get to the function g(x)=-2^(x-5)+2
flip over x-axis
right 2
down 1
The description of f(x)=|x| after it becomes g(x)=-|x-5|-3
Flipped over x-axis, shifted 5 units right, and moved down 3 units.
What is the difference between the two functions.
f(x)=(x-2)^2+4
g(x)=(x+2)^2+4
f(x) will move x^2 right two units
g(x) will move x^2 left two units