Absolute Value Graphs

Front

What is the absolute value of a number?

Back

The absolute value of a number is its distance from zero on the number line, regardless of direction. It is always non-negative.

Front

How 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

What effect does a coefficient greater than 1 have on the graph of an absolute value function?

Back

A coefficient greater than 1 makes the graph narrower compared to the parent function y = |x|.

Front

What effect does a coefficient between 0 and 1 have on the graph of an absolute value function?

Back

A coefficient between 0 and 1 makes the graph wider compared to the parent function y = |x|.

Front

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

Back

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

Front

What is the domain of the absolute value function f(x) = |x|?

Back

The domain is (-infinity, infinity).

Front

What is the range of the absolute value function f(x) = |x|?

Back

The range is [0, infinity).

Front

How does the graph of f(x) = -|x| differ from f(x) = |x|?

Back

The graph of f(x) = -|x| is a V-shaped graph that opens downwards, reflecting the graph of f(x) = |x| across the x-axis.

Front

What does the expression |x - 5| represent?

Back

It represents the distance between x and 5 on the number line.

Front

What is the effect of adding a constant outside the absolute value function, like in f(x) = |x| + 2?

Back

Adding a constant outside the absolute value function shifts the graph vertically. In this case, it shifts the graph up by 2 units.