1-3:Transforming Functions English Casbarro Unit 1: Functions

Recall: The Absolute Value Function The standard equation of the absolute 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 movement  the opposite of the sign in the parentheses k shows the up or down movement  the 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 is why it is true.

This is the same for the absolute value function also. f(x) = -|x| would be reflected across the x-axis. Because of the absolute value, you can’t tell the difference across The 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 movement  the opposite of the sign in the parentheses k shows the up or down movement  the 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 horizontal movement, 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.