Graphing Absolute Value Functions

Front

What is the general form of an absolute value function?

Back

The general form of an absolute value function is f(x) = a|x - h| + k, where (h, k) is the vertex of the graph.

Front

How does the value of 'a' affect the graph of an absolute value function?

Back

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

Front

What is the vertex of the absolute value function f(x) = -3|x + 1| + 4?

Back

The vertex is (-1, 4).

Front

What does the domain of an absolute value function typically look like?

Back

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

Front

What is the range of the function f(x) = -2|x| + 3?

Back

The range is (-∞, 3], since the maximum value occurs at the vertex.

Front

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

Back

The vertex is found at the point (h, k).

Front

What is the effect of shifting the graph of f(x) = |x| to the right by 3 units?

Back

The new function will be f(x) = |x - 3|, shifting the vertex from (0, 0) to (3, 0).

Front

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

Back

The absolute value ensures that the output is non-negative, reflecting the distance from the point t = 15.

Front

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

Back

Set the function equal to zero and solve for x.

Front

What is the relationship between the vertex and the maximum or minimum value of an absolute value function?

Back

The vertex represents the maximum value if 'a' is negative and the minimum value if 'a' is positive.