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

Solve for x: |2x - 1| = 9

Back

x = 5 and x = -4.

Front

What does the equation y = |x - 3| represent in terms of graph transformation?

Back

The graph slides to the right by 3 units.

Front

Identify the vertex of the function y = |x + 16| - 11.

Back

The vertex is (-16, -11).

Front

What is the parent function of absolute value?

Back

The parent function is f(x) = |x|.

Front

If g(x) = |x - 2|, how does it relate to the parent function?

Back

g(x) is a transformation of the parent function f(x) = |x|, shifted to the right by 2 units.

Front

What is the effect of multiplying the absolute value function by a factor greater than 1?

Back

It vertically stretches the graph away from the x-axis.

Front

What is the effect of adding a constant outside the absolute value function?

Back

It shifts the graph vertically up or down.

Front

Solve for x: |x + 4| = 3

Back

x = -1 and x = -7.

Front

What is the equation of the absolute value function that opens downwards?

Back

An example is f(x) = -|x| + k, where k is a constant.