Reality Check - Intro to Absolute Value

Front

What is absolute value?

Back

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

Front

How is the absolute value of a negative number represented?

Back

The absolute value of a negative number is represented as a positive number. For example, |-5| = 5.

Front

What is the graph of y = |x|?

Back

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

Front

What transformation occurs when the function is written as y = |x - h|?

Back

The graph of y = |x - h| shifts the graph of y = |x| to the right by h units if h is positive, and to the left by h units if h is negative.

Front

What transformation occurs when the function is written as y = |x| + k?

Back

The graph of y = |x| + k shifts the graph of y = |x| upwards by k units if k is positive, and downwards by k units if k is negative.

Front

Evaluate: |7|

Back

7

Front

Evaluate: |-3|

Back

3

Front

What is the effect of a negative sign in front of the absolute value, such as in -|x|?

Back

The negative sign in front of the absolute value reflects the graph of y = |x| across the x-axis.

Front

If f(x) = |x + 1| - 3, what is the vertex of the graph?

Back

The vertex of the graph is at the point (-1, -3).

Front

What does the expression |x - 4| represent?

Back

The expression |x - 4| represents the distance between x and 4 on the number line.