Absolute Value Study Material

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

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 range of the function f(x) = -|x|?

Back

The range of f(x) = -|x| is all real numbers less than or equal to 0, or -∞ ≤ y ≤ 0.

Front

How do you solve the inequality |x + 4| - 8 > 2?

Back

To solve |x + 4| - 8 > 2, first isolate the absolute value: |x + 4| > 10. This leads to two cases: x + 4 > 10 or x + 4 < -10, resulting in x > 6 or x < -14.

Front

What is a horizontal shift in the context of absolute value functions?

Back

A horizontal shift occurs when the input of the function is adjusted by adding or subtracting a constant, shifting the graph left or right.

Front

What is a vertical shift in the context of absolute value functions?

Back

A vertical shift occurs when a constant is added or subtracted from the entire function, shifting the graph up or down.

Front

What is the effect of multiplying an absolute value function by a positive constant?

Back

Multiplying an absolute value function by a positive constant stretches the graph vertically.

Front

What is the effect of multiplying an absolute value function by a negative constant?

Back

Multiplying an absolute value function by a negative constant reflects the graph across the x-axis and stretches it vertically.

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 at the point (3, 4).