12.6.24 Attributes of Absolute Value Functions & Piecewise Revie

Front

What is the domain of an absolute value function?

Back

The domain of an absolute value function is all real numbers, represented as D: (-∞, ∞).

Front

What is the range of an absolute value function that opens upwards?

Back

The range of an absolute value function that opens upwards is all real numbers greater than or equal to the minimum value, represented as R: [min, ∞).

Front

What is the axis of symmetry for the absolute value function f(x) = |x + 2|?

Back

The axis of symmetry is x = -2.

Front

How do you determine the minimum value of an absolute value function?

Back

The minimum value of an absolute value function occurs at the vertex of the graph, which is the point where the function changes direction.

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.

Front

What does the parameter 'a' in the absolute value function f(x) = a|x - h| + k represent?

Back

The parameter 'a' represents the vertical stretch or compression and the direction of the opening (upward if a > 0, downward if a < 0).

Front

What is the effect of changing the value of 'h' in the function f(x) = |x - h|?

Back

Changing 'h' shifts the graph horizontally. If h is positive, the graph shifts to the right; if h is negative, it shifts to the left.

Front

What is the effect of changing the value of 'k' in the function f(x) = |x - h| + k?

Back

Changing 'k' shifts the graph vertically. If k is positive, the graph shifts up; if k is negative, it shifts down.

Front

How can you identify if an absolute value function has a minimum or maximum value?

Back

An absolute value function has a minimum value at its vertex and no maximum value, as it extends infinitely upwards.

Front

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

Back

The domain is all real numbers, represented as D: (-∞, ∞).