Absolute Value Transformations

Front

What is the definition of absolute value?

Back

The absolute value of a number is its distance from zero on the number line, regardless of direction. It is denoted as |x|.

Front

What is the parent function of absolute value?

Back

The parent function of absolute value is f(x) = |x|.

Front

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

Back

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

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 f(x) = -|x|, reflects the graph across the x-axis.

Front

What does the transformation f(x) = |x - h| represent?

Back

The transformation f(x) = |x - h| represents a horizontal shift of the graph to the right by h units if h is positive, and to the left if h is negative.

Front

What does the transformation f(x) = |x| + k represent?

Back

The transformation f(x) = |x| + k represents a vertical shift of the graph upward by k units if k is positive, and downward if k is negative.

Front

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

Back

The vertex of the function f(x) = -|x + 3| + 2 is (-3, 2).

Front

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

Back

The vertex of the function f(x) = a|x - h| + k is the point (h, k).

Front

What does the transformation f(x) = |x| - 5 indicate?

Back

The transformation f(x) = |x| - 5 indicates a vertical shift of the graph downward by 5 units.

Front

What is the effect of adding a constant outside the absolute value function?

Back

Adding a constant outside the absolute value function shifts the graph vertically. For example, f(x) = |x| + 3 shifts the graph up by 3 units.