Transformation of Absolute Value Functions

Front

What is an absolute value function?

Back

An absolute value function is a function that contains an algebraic expression within absolute value symbols, denoted as f(x) = |x|, which outputs the non-negative value of x.

Front

What does a vertical stretch of a function do?

Back

A vertical stretch multiplies the output of the function by a factor greater than 1, making the graph taller.

Front

What is the effect of a horizontal shift to the left on a function?

Back

A horizontal shift to the left moves the graph of the function to the left by the specified number of units.

Front

What is the effect of a vertical shift down on a function?

Back

A vertical shift down moves the graph of the function down by the specified number of units.

Front

How do you write the absolute value function after a vertical stretch of 2 and a horizontal shift left 1?

Back

The function is written as f(x) = 2|x + 1|.

Front

What is the transformation represented by f(x) = |x - 3| + 2?

Back

This function represents a horizontal shift to the right by 3 units and a vertical shift up by 2 units.

Front

What does the negative sign in front of an absolute value function indicate?

Back

The negative sign reflects the graph of the function across the x-axis.

Front

If f(x) = |x|, what is f(-4)?

Back

f(-4) = 4.

Front

What is the transformation of f(x) = |x + 2| - 5?

Back

This function represents a horizontal shift to the left by 2 units and a vertical shift down by 5 units.

Front

How do you determine the vertex of an absolute value function?

Back

The vertex of an absolute value function f(x) = a|x - h| + k is at the point (h, k).