Transformations of 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, denoted as f(x) = |x|. It outputs the non-negative value of the expression.

Front

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

Back

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

Front

How does the graph of f(x) = |x - h| + k transform the graph of f(x) = |x|?

Back

The graph shifts horizontally by h units and vertically by k units. If h is positive, it shifts right; if negative, left. If k is positive, it shifts up; if negative, down.

Front

What is the vertex of the function f(x) = |x + 3| - 5?

Back

The vertex is at the point (-3, -5).

Front

If f(x) = |x|, what is the effect of changing it to f(x) = |x| + 2?

Back

The graph shifts up by 2 units.

Front

What happens to the graph of f(x) = |x| when it is transformed to f(x) = -|x|?

Back

The graph flips over the x-axis, creating an upside-down V shape.

Front

Describe the transformation of f(x) = |x| to f(x) = |x - 4|.

Back

The graph shifts 4 units to the right.

Front

What is the effect of the transformation f(x) = |x| - 3?

Back

The graph shifts down by 3 units.

Front

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

Back

The vertex is at the point (h, k).

Front

What does the term 'horizontal translation' mean in the context of absolute value functions?

Back

Horizontal translation refers to shifting the graph left or right along the x-axis.