Holy SHIFT!
Given the parent function: f(x) = x2
Name the shift that would occur in g(x) = x2 +4
up (4 units)
When the negative sign is OUTSIDE of the parentheses, the graph will reflect over the ___ axis
X
If we multiply a function by a number GREATER THAN 1 (ex: y = 4x2 ), the result will be a vertical ________
STRETCH
when a function undergoes a change in position or size it is called a _____________________
TRANSFORMATION
In a horizontal compression, the graph is "squeezed" towards the y axis by multiplying "x" by a number that is ____________________ than 1.
GREATER
ex: y=(3x)2
Given the parent function: f(x) = x2
Name the shift that would occur in g(x) = x2 - 7
down (7 units)
Y
If we multiply a function by a number between 0-1 (ex: y=1/3x2 ), the result will be a vertical ______________ (squish!)
COMPRESSION
Starting function in its simplest form
PARENT FUNCTION
ODD functions reflect through the ________
ORIGIN
Name the TWO transformations that occur when the parent graph y = x2 becomes y = (x+4)2+6
left (4 units) and up (6 units)
When a function reflects over the x axis, the ___ values stay the same and the ____ values change their sign.
x values
y values
Describe the transformation of the following function:
f(x) = 4f(x)
(vertical stretch or vertical compression? / By what value? / Narrower or wider?)
vertical stretch by 4 (narrower)
When a graph "flips" over the x or y axis, it is called a _____________________________
REFLECTION
EVEN functions reflect over the y axis, causing the ___ value to change it's sign.
X
Name the TWO shifts that occur when y=lxl becomes y=lx+3l-2
left (3 units) and down (2 units)
When a function reflects over the y axis, the ____ values stay the same and the _____ values change their sign.
y values
x values
If the point (-5,12) lies on the graph of y = f(x), What point must lie on the graph of y = 1/2f(x)?
(-5, 6)
(keep the x, multiply the y by 1/2)
The number of increments that a function moves to the left, right, up, or down are called ________________
UNITS
TRUE OR FALSE: A horizontal STRETCH will multiply x by a number that is 0<x<1
TRUE
ex: y = (1/2x)2
Using the parent function y =x2
create an equation that shifts the parent left 7 units and up 4 units
y = (x+7)2 + 4
Name the THREE transformations that occur when the parent y = x2 is transformed to y = - (x-6)2 - 5
reflection over x axis
shift right 6 units
shift down 5 units
If the point (3,-10) lies on the graph of y = g(x), then which point MUST lie on the graph of y = 3g(x)?
(3, -30)
keep the x, multiply the y by 3
When a function becomes narrower, it is a vertical __________ and when it becomes wider, it is a vertical _________________.
STRETCH
COMPRESSION
If f(x) = x2 , write the equation for f(x) after it has been translated 2 units to the right, vertically stretched by a factor of 4, reflected over the x-axis, and moved up 5.
f(x) = -4(x-2)2 +5