Absolute Value & Square Root Functions

Front

What is the Absolute Value Function?

Back

The Absolute Value Function is defined as f(x) = |x|, which measures the distance of a number from zero on the number line, always resulting in a non-negative value.

Front

What does it mean to compress a function?

Back

To compress a function means to make it narrower. For example, if the function f(x) = |x| is transformed to f(x) = 2|x|, it compresses the graph vertically.

Front

What does it mean to shift a function up or down?

Back

Shifting a function up or down involves adding or subtracting a constant from the function. For example, f(x) = |x| + 4 shifts the graph up 4 units.

Front

What is the parent function of Absolute Value?

Back

The parent function of Absolute Value is f(x) = |x|, which has a V-shaped graph that opens upwards.

Front

What is the range of the Absolute Value Function?

Back

The range of the Absolute Value Function is y ≥ 0, meaning it includes all non-negative values.

Front

How do you determine the transformations of a function?

Back

To determine the transformations, analyze the changes in the function's equation compared to its parent function, looking for shifts, stretches, or reflections.

Front

What does it mean to reflect a function across the x-axis?

Back

Reflecting a function across the x-axis means to invert its output values. For example, f(x) = -|x| reflects the Absolute Value Function downwards.

Front

What is the effect of a negative sign in front of the Absolute Value Function?

Back

A negative sign in front of the Absolute Value Function, such as f(x) = -|x|, reflects the graph across the x-axis.

Front

What is a square root function?

Back

A square root function is defined as f(x) = √x, which represents the principal square root of x and is only defined for x ≥ 0.

Front

What is the domain of the square root function?

Back

The domain of the square root function f(x) = √x is x ≥ 0, meaning it includes all non-negative real numbers.