Absolute Value Functions

Front

What is the vertex of the absolute value function?

Back

The vertex of the absolute value function is the point where the graph changes direction. For the function f(x) = |x| + 4, the vertex is at (0, 4).

Front

What is the domain of the absolute value function?

Back

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

Front

What is the equation of the absolute value function that has a vertex at (0, 4)?

Back

The equation is f(x) = |x| + 4.

Front

What is the maximum value of the function f(t) = -2|t - 15| + 50?

Back

The maximum sales for one week is $50,000.

Front

What is the range of the absolute value function?

Back

The range of the absolute value function is all real numbers greater than or equal to the vertex's y-coordinate. For f(x) = |x| + 4, the range is [4, ∞).

Front

How does the graph of f(x) = |x| + 4 differ from f(x) = |x|?

Back

The graph of f(x) = |x| + 4 is shifted upward by 4 units compared to f(x) = |x|.

Front

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

Back

A negative coefficient reflects the graph across the x-axis. For example, f(x) = -|x| opens downward.

Front

What is the significance of the absolute value in a function?

Back

The absolute value ensures that the output is always non-negative, representing distance from zero.

Front

How do you find the x-intercepts of an absolute value function?

Back

To find the x-intercepts, set the function equal to zero and solve for x.

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.