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1-3:Transforming Functions

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.

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1-3:Transforming Functions

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

  2. 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.

  3. The absolute value graph and transformations f(x)= a|x– h| + k k shows the up or down movement the same sign That the k shows • a is the same a from the standard form of the equation it will show • whether it’s up or down • how wide or narrow it is h shows the left or right movement the opposite of the sign in the parentheses

  4. 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|.

  5. 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.

  6. 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.

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

  8. Quadratic Equations behave the same way. f(x)= a(x – h)2 + k k shows the up or down movement the same sign That the k shows h shows the left or right movement the opposite of the sign in the parentheses • a is the same a from the standard form of the equation it will show • whether it’s up or down • how wide or narrow it is

  9. 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. Moves the graph up or down k units (sign agrees with move) How the graph is stretched or compressed Moves the graph left or right (sign is opposite the move) Rational Functions also use the same transformation rules.

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