Absolute Value Functions and Transformations

Front

What is the definition of an absolute value function?

Back

An absolute value function is a function that outputs the distance of a number from zero on the number line, denoted as f(x) = |x|.

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?

Back

The graph shifts horizontally to the right by h units and vertically by k units.

Front

What is the effect of a negative sign in front of an absolute value function, such as f(x) = -|x|?

Back

The negative sign reflects the graph of the absolute value function across the x-axis.

Front

What does the vertex of an absolute value function represent?

Back

The vertex represents the minimum or maximum point of the function, depending on the direction it opens.

Front

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

Back

The vertex is found at the point (-3, -2).

Front

What transformation does the equation f(x) = |x| + 5 represent?

Back

This represents a vertical translation of the graph upwards by 5 units.

Front

What is the transformation for the function f(x) = |x - 4|?

Back

This represents a horizontal translation of the graph to the right by 4 units.

Front

If f(x) = |x|, what is the value of f(-3)?

Back

f(-3) = 3, since the absolute value of -3 is 3.

Front

What is the general form of an absolute value function?

Back

The general form is f(x) = a|x - h| + k, where (h, k) is the vertex.