Absolute Value Review

Front

What is the definition of absolute value?

Back

The absolute value of a number is its distance from zero on the number line, regardless of direction. It is denoted as |x|.

Front

What is the vertex of the function y = 4|x| + 1?

Back

The vertex is (0, 1).

Front

How do you find the vertex of an absolute value function in the form y = a|x - h| + k?

Back

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

Front

What is the equation of the graph that opens downwards and has a vertex at (2, 4)?

Back

The equation is y = -|x - 2| + 4.

Front

Solve the equation |6 - 2k| = 18. What are the possible values of k?

Back

k = -6 or k = 12.

Front

What is the solution set for the equation |−4 + 5x| = 16?

Back

x = -12/5 or x = 4.

Front

What does the graph of y = |x| look like?

Back

It is a V-shaped graph that opens upwards with the vertex at the origin (0, 0).

Front

How does the value of 'a' in y = a|x| affect the graph?

Back

If 'a' is positive, the graph opens upwards; if 'a' is negative, it opens downwards.

Front

What is the effect of adding a constant 'k' to the absolute value function y = |x|?

Back

Adding 'k' shifts the graph vertically by 'k' units.

Front

What is the effect of subtracting a constant 'k' from the absolute value function y = |x|?

Back

Subtracting 'k' shifts the graph vertically down by 'k' units.