Absolute Value Functions

Front

What is the definition of an absolute value function?

Back

An absolute value function is a function that outputs the distance of a number from zero on the number line, regardless of direction. It is defined as f(x) = |x|.

Front

What is the vertex of the absolute value function y = |x|?

Back

The vertex of the function y = |x| is at the point (0, 0).

Front

How does the graph of y = -|x| differ from y = |x|?

Back

The graph of y = -|x| is a reflection of the graph of y = |x| over the x-axis.

Front

What transformation does the equation y = |x - 3| represent?

Back

The equation y = |x - 3| represents a horizontal shift of the parent function y = |x| to the right by 3 units.

Front

What is the effect of adding a constant outside the absolute value function, such as in y = |x| + 4?

Back

Adding a constant outside the absolute value function results in a vertical shift of the graph upward by that constant value.

Front

What does the equation y = -|x| + 2 represent in terms of transformations?

Back

The equation y = -|x| + 2 represents a reflection over the x-axis and a vertical shift upward by 2 units.

Front

How do you find the vertex of the function y = |x - 2| + 3?

Back

The vertex of the function y = |x - 2| + 3 is at the point (2, 3).

Front

What is the general form of an absolute value function?

Back

The general form of an absolute value function is f(x) = a|bx - h| + k, where (h, k) is the vertex.

Front

What transformation does the equation y = |x + 1| - 5 represent?

Back

The equation y = |x + 1| - 5 represents a horizontal shift to the left by 1 unit and a vertical shift downward by 5 units.

Front

What is the effect of a negative coefficient in front of the absolute value, such as in y = -|x + 2|?

Back

A negative coefficient in front of the absolute value reflects the graph over the x-axis.