Absolute Value Functions (Graphs and Transformations)

Front

What is the definition of an absolute value function?

Back

An absolute value function is a function that returns the non-negative value of a number, denoted as f(x) = |x|, where |x| is the absolute value of x.

Front

What is the graph of the parent function of an absolute value function?

Back

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

Front

What is the domain of the absolute value function f(x) = |x|?

Back

The domain of f(x) = |x| is all real numbers, expressed as (-∞, ∞).

Front

What is the range of the absolute value function f(x) = |x|?

Back

The range of f(x) = |x| is all non-negative real numbers, expressed as [0, ∞).

Front

How does the graph of f(x) = |x - 3| + 2 differ from the parent function?

Back

The graph of f(x) = |x - 3| + 2 is the parent function shifted 3 units to the right and 2 units up.

Front

What effect does the negative sign have in the function f(x) = -|x|?

Back

The negative sign reflects the graph of the absolute value function across the x-axis, resulting in an upside-down V shape.

Front

What is the vertex of the function f(x) = |x + 4| - 3?

Back

The vertex of the function f(x) = |x + 4| - 3 is at the point (-4, -3).

Front

What transformation does the function f(x) = |x| + 5 represent?

Back

The function f(x) = |x| + 5 represents a vertical shift of the parent function f(x) = |x| upwards by 5 units.

Front

What is the effect of the coefficient in front of the absolute value in f(x) = 2|x|?

Back

The coefficient 2 vertically stretches the graph of the absolute value function, making it steeper.

Front

How do you find the x-intercepts of the function f(x) = |x - 2|?

Back

To find the x-intercepts, set f(x) = 0: |x - 2| = 0, which gives x = 2.