Transformations of Absolute Value Functions

Front

What is an absolute value function?

Back

An absolute value function is a function that contains an absolute value expression. It is defined as f(x) = |x|, which outputs the non-negative value of x.

Front

What is the general form of an absolute value function?

Back

The general form is f(x) = a|bx - h| + k, where (h, k) is the vertex, 'a' determines the direction and steepness, and 'b' affects the width of the graph.

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 absolute value of 'a' affects the steepness of the graph.

Front

What does the vertex of an absolute value function represent?

Back

The vertex is the highest or lowest point of the graph, depending on whether it opens upwards or downwards.

Front

How do you find the vertex of the function f(x) = -2|x - 3| + 5?

Back

The vertex is at the point (3, 5) because it is in the form f(x) = a|x - h| + k, where (h, k) is the vertex.

Front

What effect does the term 'h' have in the function f(x) = |x - h|?

Back

The term '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 effect does the term 'k' have in the function f(x) = |x| + k?

Back

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

Front

What is the equation of the absolute value function that opens downwards with vertex (2, 4)?

Back

The equation is f(x) = -|x - 2| + 4.

Front

How do you determine the direction of the graph of f(x) = -|x| + 3?

Back

The negative sign in front of the absolute value indicates that the graph opens downwards.

Front

What is the effect of a vertical shift on the graph of an absolute value function?

Back

A vertical shift moves the graph up or down without changing its shape.