Parent Function Transformations

Front

What is a parent function?

Back

A parent function is the simplest form of a function type, which serves as a foundation for more complex functions. Examples include linear functions (y = x), quadratic functions (y = x²), and absolute value functions (y = |x|).

Front

What transformation occurs when a function is translated up?

Back

When a function is translated up, the y-values of the function increase by a certain amount. For example, the function y = f(x) becomes y = f(x) + k, where k is a positive number.

Front

What transformation occurs when a function is translated down?

Back

When a function is translated down, the y-values of the function decrease by a certain amount. For example, the function y = f(x) becomes y = f(x) - k, where k is a positive number.

Front

What transformation occurs when a function is translated left?

Back

When a function is translated left, the x-values of the function decrease by a certain amount. For example, the function y = f(x) becomes y = f(x + k), where k is a positive number.

Tags

CCSS.HSF.BF.B.3

Front

What transformation occurs when a function is translated right?

Back

When a function is translated right, the x-values of the function increase by a certain amount. For example, the function y = f(x) becomes y = f(x - k), where k is a positive number.

Front

What is the effect of a vertical stretch on a function?

Back

A vertical stretch occurs when the output values of a function are multiplied by a factor greater than 1. For example, the function y = f(x) becomes y = a * f(x), where a > 1.

Front

What is the effect of a vertical compression on a function?

Back

A vertical compression occurs when the output values of a function are multiplied by a factor between 0 and 1. For example, the function y = f(x) becomes y = a * f(x), where 0 < a < 1.

Front

What is the effect of a horizontal stretch on a function?

Back

A horizontal stretch occurs when the input values of a function are multiplied by a factor greater than 1. For example, the function y = f(x) becomes y = f(b * x), where b > 1.

Front

What is the effect of a horizontal compression on a function?

Back

A horizontal compression occurs when the input values of a function are multiplied by a factor between 0 and 1. For example, the function y = f(x) becomes y = f(b * x), where 0 < b < 1.

Front

How does the absolute value function transform?

Back

The absolute value function, y = |x|, reflects all negative y-values to positive, creating a V-shape graph.