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 f(x) = |x|.

Front

How does the graph of f(x) = |x| look?

Back

The graph of f(x) = |x| is a V-shaped graph that opens upwards, with its vertex at the origin (0,0).

Front

What effect does a positive coefficient have on the absolute value function?

Back

A positive coefficient stretches the graph vertically, making it steeper.

Front

What effect does a negative coefficient have on the absolute value function?

Back

A negative coefficient reflects the graph across the x-axis, making it open downwards.

Front

What does the expression |x - h| represent in an absolute value function?

Back

The expression |x - h| represents a horizontal shift of the graph to the right by h units if h is positive, and to the left by h units if h is negative.

Front

What does the expression |x| + k represent in an absolute value function?

Back

The expression |x| + k represents a vertical shift of the graph upwards by k units if k is positive, and downwards by k units if k is negative.

Front

What is the line of symmetry for the absolute value function f(x) = |x|?

Back

The line of symmetry for the function f(x) = |x| is the y-axis, or x = 0.

Front

How do you find the vertex of the absolute value function f(x) = a|x - h| + k?

Back

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

Front

What transformation occurs in the function f(x) = |x + 3| - 2?

Back

The function f(x) = |x + 3| - 2 shifts the graph left 3 units and down 2 units.