Absolute Value Functions

Front

What is the definition of an absolute value function?

Back

An absolute value function is a function that contains an algebraic expression within absolute value symbols, which measures the distance of a number from zero on the number line, always resulting in a non-negative output.

Front

What is the parent function of absolute value?

Back

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

Front

What is the vertex of the 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| change when a constant is added outside the absolute value?

Back

Adding a constant outside the absolute value shifts the graph vertically. For example, y = |x| + 3 shifts the graph up by 3 units.

Front

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

Back

A negative sign in front of an absolute value function reflects the graph across the x-axis. For example, y = -|x| opens downward.

Front

Describe the transformation of the function y = |x - 3| + 2 from the parent function y = |x|.

Back

The function y = |x - 3| + 2 is shifted right 3 units and up 2 units from the parent function.

Front

What is the line of symmetry for the function y = |x + 4|?

Back

The line of symmetry for the function y = |x + 4| is x = -4.

Front

How do you find the vertex of the function y = a|x - h| + k?

Back

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

Front

What does the 'a' value in the function y = a|x - h| + k represent?

Back

The 'a' value represents the vertical stretch or compression and the direction of the opening of the graph. If 'a' is positive, the graph opens upwards; if negative, it opens downwards.

Front

What is the effect of the transformation y = |x + 2| - 5 on the graph of y = |x|?

Back

The transformation y = |x + 2| - 5 shifts the graph left 2 units and down 5 units.