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 general form of an absolute value function?

Back

The general form is f(x) = a|x - h| + k, where (h, k) is the vertex of the graph, 'a' determines the direction and steepness of the graph.

Front

What does the parameter 'a' in the absolute value function affect?

Back

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

Front

How does the transformation 'right 3' affect the graph of f(x) = |x|?

Back

The transformation 'right 3' shifts the graph of f(x) = |x| three units to the right, resulting in the function f(x) = |x - 3|.

Front

How does the transformation 'up 2' affect the graph of f(x) = |x|?

Back

The transformation 'up 2' shifts the graph of f(x) = |x| two units upwards, resulting in the function f(x) = |x| + 2.

Front

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

Back

The range of f(x) = |x| is all real numbers y such that y ≥ 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, or (-∞, ∞).

Front

What does flipping over the x-axis do to the graph of an absolute value function?

Back

Flipping over the x-axis reflects the graph across the x-axis, changing the function to f(x) = -|x|.

Front

What does flipping over the y-axis do to the graph of an absolute value function?

Back

Flipping over the y-axis reflects the graph across the y-axis, which does not change the graph of an absolute value function since it is symmetric about the y-axis.

Front

If f(x) = |x - 5|, what is the vertex of the graph?

Back

The vertex of the graph is at the point (5, 0).