3.7 Graphing Absolute Value Functions

Front

What is 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 value.

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 vertical stretch or compression and the direction of the opening.

Front

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

Back

If 'a' is positive, the graph opens upwards; if 'a' is negative, it opens downwards. The larger the absolute value of 'a', the steeper the graph.

Front

What is the vertex of the function f(x) = 2|x + 3| - 1?

Back

The vertex is (-3, -1).

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 does the graph of f(x) = |x| look like?

Back

The graph is a V-shape that opens upwards with the vertex at the origin (0, 0).

Front

What is the effect of shifting the graph of f(x) = |x| to the right by 2 units?

Back

The new function is f(x) = |x - 2|, and the vertex shifts to (2, 0).

Front

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

Back

The new function is f(x) = |x| + 3, and the vertex shifts to (0, 3).

Front

What is the equation of the absolute value function that has a vertex at (1, -2) and opens downwards?

Back

The equation is f(x) = -a|x - 1| - 2, where 'a' is a positive constant.

Front

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

Back

Set the function equal to zero and solve for x. For example, for f(x) = |x - 2|, set |x - 2| = 0, giving x = 2.