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.

Tags

CCSS.HSF-IF.C.7D

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.

Tags

CCSS.HSF-IF.C.7D

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).

Tags

CCSS.HSF-IF.C.7D

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).

Tags

CCSS.HSF-IF.C.7D

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).

Tags

CCSS.HSF-IF.C.7D

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.

Tags

CCSS.HSF-IF.C.7D

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.

Tags

CCSS.HSF-IF.C.7D