Absolute Value: Characteristics, Transformations & Mappings

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|, which forms a V-shape on the graph.

Front

How does a negative coefficient affect the graph of an absolute value function?

Back

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

Front

What does it mean to stretch an absolute value function vertically?

Back

Stretching an absolute value function vertically means multiplying the function by a factor greater than 1, which makes the V-shape narrower.

Front

What does it mean to compress an absolute value function vertically?

Back

Compressing an absolute value function vertically means multiplying the function by a factor between 0 and 1, which makes the V-shape wider.

Front

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

Back

Adding a constant to an absolute value function shifts the graph vertically. If the constant is positive, it shifts up; if negative, it shifts down.

Front

What is the effect of subtracting a constant from the input of an absolute value function?

Back

Subtracting a constant from the input of an absolute value function shifts the graph horizontally. If the constant is positive, it shifts left; if negative, it shifts right.

Front

How do you identify transformations in the function f(x) = -rac{1}{4}|x| + 6?

Back

This function is inverted (due to the negative sign), vertically compressed (by a factor of 1/4), and shifted up 6 units.

Front

What does the notation |x - 2| represent in a function?

Back

The notation |x - 2| represents the absolute value of the expression (x - 2), indicating the distance of x from 2.

Front

What is the transformation of the function f(x) = |x| when it becomes g(x) = |x + 3|?

Back

The function g(x) = |x + 3| is the result of shifting the graph of f(x) = |x| left by 3 units.