Transformations of Linear Functions

Front

What is a vertical shrink in the context of linear functions?

Back

A vertical shrink occurs when the output values of a function are multiplied by a factor less than 1, causing the graph to become flatter.

Front

How does the equation g(x) = 1/2f(x) + 11 transform the parent function f(x) = x?

Back

It results in a vertical shrink by a factor of 1/2 and a vertical shift upward by 11 units.

Front

What does the equation y = f(x) + c represent in terms of transformations?

Back

It represents a vertical shift of the graph of f(x) upward by c units if c is positive and downward if c is negative.

Front

What transformation is represented by the equation y = -3f(x) + 5?

Back

This equation represents a reflection over the x-axis, a vertical stretch by a factor of 3, and a vertical shift upward by 5 units.

Front

If the graph of f(x) = x is shifted 7 units up and horizontally compressed by a factor of 3, what is the resulting function?

Back

The resulting function is g(x) = f(3x) + 7.

Front

What is a reflection over the x-axis in the context of function transformations?

Back

A reflection over the x-axis occurs when the output values of a function are multiplied by -1, flipping the graph upside down.

Front

What does a vertical stretch by a factor of 2 mean for the function f(x)?

Back

It means that the output values of the function are multiplied by 2, making the graph steeper.

Front

How does the transformation f(x) = 2f(x) affect the graph of the parent function?

Back

It results in a vertical stretch by a factor of 2, making the graph steeper.

Front

What is the effect of a horizontal compression by a factor of k on the function f(x)?

Back

A horizontal compression by a factor of k means that the input values are multiplied by k, making the graph narrower.

Front

What does the term 'parent function' refer to in transformations?

Back

The parent function is the simplest form of a function in a family of functions, serving as a reference for transformations.