Absolute Value Functions Graphs

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|. It outputs the non-negative value of x.

Front

How does a vertical stretch affect the graph of an absolute value function?

Back

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

Front

What does a horizontal shift to the left by 1 unit look like in an absolute value function?

Back

A horizontal shift left by 1 unit is represented as f(x) = |x + 1|, moving the vertex of the graph to the left.

Front

What is the effect of a vertical shift down by 9 units on the graph of an absolute value function?

Back

A vertical shift down by 9 units is represented as f(x) = |x| - 9, moving the entire graph down by 9 units.

Front

What is the vertex of the function f(x) = 2|x + 1| - 9?

Back

The vertex of the function f(x) = 2|x + 1| - 9 is at the point (-1, -9).

Front

How do you identify the graph of f(x) = -|x + 1| + 4?

Back

The graph of f(x) = -|x + 1| + 4 is a downward-opening V shape with its vertex at (-1, 4).

Front

What does the equation y = |x + 2| + 1 represent graphically?

Back

The equation y = |x + 2| + 1 represents a V-shaped graph with its vertex at (-2, 1).

Front

What is the graph of y = |x| - 2?

Back

The graph of y = |x| - 2 is a V shape with its vertex at (0, -2).

Front

How can you determine the transformations applied to the graph of y = |x|?

Back

Transformations can be determined by analyzing changes in the function's equation, such as shifts, stretches, and reflections.

Front

What does the absolute value symbol indicate in a function?

Back

The absolute value symbol indicates that the output will always be non-negative, regardless of the input's sign.