1-3:Transforming Functions

1-3:Transforming Functions

English CasbarroUnit 1: Functions

Recall: The Absolute Value Function

The standard equation of theabsolute value function is:

f(x) = | x |

It intersects the coordinate plane at the origin.

It is also called a parent function.

The absolute value graph and transformations

f(x)= a|x – h| + k

a is the same a from the standard form of the equation it will show

1) whether it’s up or down

2) how wide or narrow it is

h shows the left or right movementthe opposite of the sign in the parentheses

k shows the upor down movementthe same sign That the k shows

So, the function f(x) = 3|x| would be steeper than the parent function f(x) =|x|.

The function f(x) = ½ |x| would be “flatter” than the parent function f(x) = |x|.

This corresponds to all of the other functions that we will be studying.When you are dealing with a basic function, this is what happens, so this iswhy it is true.

This is the same for the absolute value function also. f(x) = -|x| would be reflected across the x-axis. Becauseof the absolute value, you can’t tell the difference acrossThe y-axis. The next page shows this with a line.

Example 4

The parent function f(x) = |x| is stretched by a factor of 5, translated 5 units left, and 2 units up to create g(x).

Now you try:

Use the description to write the absolute value function.

1. The parent function f(x) = |x| is vertically compressed by a factor of 1/3 and translated 2 units right and 4 units down to create g.

2. The parent function f(x) = |x| is reflected across the x-axis and translated 5 units left and 1 unit up to create g.

Quadratic Equations behave the same way.

f(x)= a(x – h)2 + k

a is the same a from the standard form of the equation it will show

1) whether it’s up or down

2) how wide or narrow it is

h shows the left or right movementthe opposite of the sign in the parentheses

k shows the upor down movementthe same sign That the k shows

The parent function of rational functions is . The function

below should look familiar. The a is still the vertical stretch or compression.The k is still the vertical translation up or down. And the h is still the horizontalmovement, the opposite of the sign that you see.

How the graph is stretched or compressed

Moves the graph up or down k units (sign agrees with move)

Moves the graph left or right (sign is opposite the move)

Rational Functions also use the same transformation rules.