Precalculus Transformation of Functions

Front

What is a horizontal translation in the context of function transformations?

Back

A horizontal translation shifts the graph of a function left or right along the x-axis.

Front

If the point (8,5) on the graph of y=f(x) moves to (16,5), what type of transformation has occurred?

Back

A horizontal translation 8 units to the right.

Front

What does a reflection over the y-axis indicate about the transformation of a function?

Back

It indicates that for every point (x,y) on the graph, the point (-x,y) is also on the graph.

Front

Describe the transformation represented by the function f(1/4x).

Back

A horizontal stretch by a factor of 4.

Front

What is the effect of a reflection over the x-axis on the graph of a function?

Back

It changes the sign of the y-coordinates of all points on the graph.

Front

What does the notation y=(x-2)^3 + 4 represent in terms of transformations?

Back

A horizontal shift 2 units to the right and a vertical shift 4 units up.

Front

How does a vertical translation affect the graph of a function?

Back

It shifts the graph up or down along the y-axis.

Front

What is the general effect of multiplying the input of a function by a factor greater than 1?

Back

It results in a horizontal compression of the graph.

Front

What is the difference between a horizontal stretch and a horizontal compression?

Back

A horizontal stretch increases the distance between points on the graph, while a horizontal compression decreases it.

Front

What transformation occurs when a function is written as f(x) + k?

Back

A vertical translation k units up if k is positive, and k units down if k is negative.