Transforming
Functions
Functions
Starting with the parent function y=x^2, describe the transformation of the following function: y=x^2+3.
Translate 3 units up.
What is the parent function for a quadratic function?
y=x^2
What is the parent function of the absolute value function?
y=|x|
Switch the places of the x and y variable
What is the end behavior of a function with a negative leading coefficient to an odd degree?
As x approaches -inf, f(x) approaches inf. As x approaches inf, f(x) approaches -inf.
Starting with the parent function y=x^2, describe the transformation of the following function: y=x^2-7.
Translate 7 units down.
What is the general form of a quadratic function?
y=ax^2+bx+c
What letter does the graph of an absolute value function look like?
It looks like a "v".
Find the inverse of the following function: y=3x+1
y=(x-1)/3
What is the end behavior of a function with a positive leading coefficient to an odd degree?
As x approaches -inf, f(x) approaches -inf. As x approaches inf, f(x) approaches inf.
Starting with the parent function y=x^2, describe the transformation of the following function: y=(x+5)^2.
Translate 5 units to the left.
What is the vertex form of a quadratic function?
y=a(x-h)^2+k
Solve the absolute value equation for x: |x+2|=4
x=-6 and x=2
What requirement does a function have to meet in order to take its inverse?
It must be one-to-one.
What is the end behavior of a function with a negative leading coefficient to an even degree?
As x approaches -inf, f(x) approaches -inf. As x approaches inf, f(x) approaches -inf.
Starting with the parent function y=x^2, describe the transformation of the following function: y=(x-11)^2.
Translate 11 units to the right.
Factor the following function: y=x^2+10x+16
y=(x+2)(x+8)
Solve the absolute value equation for x: |2x+3|-5=18
How do we notate the inverse of f(x)?
f^-1(x)
What is the end behavior of a function with a positive leading coefficient to an even degree?
As x approaches -inf, f(x) approaches inf. As x approaches inf, f(x) approaches inf.
Starting with the parent function y=x^2, describe the transformation of the following function: y=4x^2.
Stretch vertically by a factor of 4.
Factor using complete the square: y=x^2-2x+4
y=(x-1)^2+3
Solve the absolute value equation for x: 2|2x-1|=6
x=-1 and x=2
Given the coordinate pair (-3,9), what are the inverse coordinates?
(9,-3)
Is the parent function y=x^2 concave up or concave down?
Concave up