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.

Tags

CCSS.HSF-IF.C.7D

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).

Tags

CCSS.HSF-IF.C.7D

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).

Tags

CCSS.HSF-IF.C.7D

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).

Tags

CCSS.HSF-IF.C.7D

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.