Parent Graphs

Front

What is a parent graph?

Back

A parent graph is the simplest form of a function, which serves as a base for transformations.

Front

What is the parent function for absolute value?

Back

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

Front

What happens when you add a constant to the end of a function?

Back

Adding a constant shifts the graph vertically. If the constant is positive, it shifts up; if negative, it shifts down.

Front

What does g(x) = |x - 2| represent?

Back

This represents a horizontal shift of the parent function f(x) = |x| to the right by 2 units.

Front

How does the equation f(x) = |x| + 3 transform the parent function?

Back

This shifts the graph of the parent function f(x) = |x| up by 3 units.

Front

What is the domain of the function f(x) = |x|?

Back

The domain of f(x) = |x| is all real numbers, or (-∞, ∞).

Front

What is the end behavior of the graph of f(x) = |x|?

Back

As x → ∞, y → ∞ and as x → -∞, y → ∞.

Front

What does it mean to shift a graph 3 units to the right?

Back

It means to replace x with (x - 3) in the function.

Front

What is the effect of a negative sign in front of the absolute value function?

Back

It 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 [0, ∞).