Graphing 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 does the graph of y = |x| look like?

Back

The graph of y = |x| is a V-shaped graph that opens upwards, with its vertex at the origin (0,0).

Front

How does the graph of y = |x - h| change when h is positive?

Back

When h is positive, the graph of y = |x - h| shifts to the right by h units.

Front

How does the graph of y = |x + h| change when h is negative?

Back

When h is negative, the graph of y = |x + h| shifts to the left by |h| units.

Front

What effect does a negative sign in front of the absolute value have on the graph?

Back

A negative sign in front of the absolute value, such as in y = -|x|, reflects the graph over the x-axis.

Front

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

Back

The vertex of the function f(x) = |x - 3| is at the point (3, 0).

Front

What does the term 'translation' mean in the context of graphing functions?

Back

Translation refers to shifting the graph of a function horizontally or vertically without changing its shape.

Front

What is the effect of adding a constant to the absolute value function, such as in f(x) = |x| + k?

Back

Adding a constant k to the absolute value function shifts the graph vertically by k units. If k is positive, it shifts up; if k is negative, it shifts down.

Front

How do you determine the transformations of the function f(x) = |x - 5| - 2?

Back

The function f(x) = |x - 5| - 2 is translated right 5 units and down 2 units.

Front

What is the general form of an absolute value function?

Back

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