Absolute Value Functions

Front

What is absolute value?

Back

The absolute value of a number is its distance from zero on the number line, always expressed as a positive value.

Front

Why is absolute value always positive?

Back

Absolute value is talking about distance, and distance is always measured by positive numbers.

Front

What is the vertex of the absolute value function f(x) = |2x - 6| + 4?

Back

The vertex is (3, 4).

Front

How do you shift the graph of y = |x| to the right by 4 units?

Back

The transformation is represented by the function y = |x - 4|.

Front

What does the vertex of an absolute value function represent?

Back

The vertex represents the minimum or maximum point of the graph, depending on its orientation.

Front

What is the general form of an absolute value function?

Back

The general form is f(x) = a|bx - h| + k, where (h, k) is the vertex.

Front

What transformation occurs in the function f(x) = |x| + 5?

Back

This function shifts the graph of y = |x| up by 5 units.

Front

What transformation occurs in the function f(x) = |x - 2| - 3?

Back

This function shifts the graph of y = |x| right by 2 units and down by 3 units.

Front

What is the effect of the coefficient 'a' in the function f(x) = a|x|?

Back

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

Front

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

Back

The vertex is (0, 0).