Absolute Value Functions Review

Front

What is the parent function of absolute value?

Back

The parent function of absolute value is y = |x|.

Front

How does the graph of y = |x + c| transform compared to y = |x|?

Back

The graph shifts left by c units if c is positive and right by c units if c is negative.

Front

What effect does a negative sign in front of an absolute value function have?

Back

It reflects the graph across the x-axis.

Front

What does a vertical stretch by a factor of k do to the graph of y = |x|?

Back

It makes the graph steeper, stretching it vertically by a factor of k.

Front

How does a vertical shift of d units affect the graph of y = |x|?

Back

It shifts the graph up by d units if d is positive and down by d units if d is negative.

Front

What is the transformation of the function y = |x| + 3?

Back

The graph of y = |x| + 3 is shifted up 3 units.

Front

Describe the transformation of the function y = -|x - 4|. What does the negative sign indicate?

Back

The graph is reflected across the x-axis and shifted right 4 units.

Front

What is the effect of a horizontal shift in the absolute value function?

Back

A horizontal shift moves the graph left or right depending on the sign of the constant added or subtracted inside the absolute value.

Front

How do you write an absolute value function that reflects across the x-axis and shifts vertically?

Back

The function can be written as y = -|x - h| + k, where h is the horizontal shift and k is the vertical shift.

Front

What does the notation |x + 2| represent in terms of transformations?

Back

It represents a left shift of 2 units from the parent function y = |x|.