Algebra 1: Chapter 5 (Absolute Value)

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 parent function of absolute value?

Back

The parent function of absolute value is f(x) = |x|.

Front

How does the graph of f(x) = |x| look?

Back

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

Front

What effect does a negative sign have in front of an absolute value function?

Back

A negative sign in front of an absolute value function reflects the graph across the x-axis.

Front

What is the vertex of the function f(x) = |x - 3| + 4?

Back

The vertex of the function f(x) = |x - 3| + 4 is (3, 4).

Front

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

Back

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

Front

What does the 'a' value represent in the function f(x) = a|x - h| + k?

Back

The 'a' value represents the vertical stretch or compression and the direction of the graph (upward if a > 0, downward if a < 0).

Front

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

Back

Adding a constant outside the absolute value function shifts the graph vertically. For example, f(x) = |x| + 2 shifts the graph up by 2 units.

Front

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

Back

Adding a constant inside the absolute value function shifts the graph horizontally. For example, f(x) = |x + 2| shifts the graph left by 2 units.

Front

How do you solve the equation |x - 5| = 3?

Back

To solve |x - 5| = 3, set up two equations: x - 5 = 3 and x - 5 = -3. The solutions are x = 8 and x = 2.