Transformations of Linear Functions

Front

What is a transformation of a function?

Back

A transformation of a function refers to a change in the position, size, or shape of its graph, which can include translations, reflections, stretches, and compressions.

Tags

CCSS.HSF.BF.B.3

Front

What is the parent function of linear functions?

Back

The parent function of linear functions is y = x.

Front

What does a horizontal translation of a graph involve?

Back

A horizontal translation involves shifting the graph left or right along the x-axis.

Front

How does the graph of g = f(x - 4) relate to f(x)?

Back

The graph of g is a horizontal translation of the graph of f, 4 units to the right.

Front

What does a vertical translation of a graph involve?

Back

A vertical translation involves shifting the graph up or down along the y-axis.

Front

What effect does multiplying a function by a negative number have on its graph?

Back

Multiplying a function by a negative number reflects the graph over the x-axis.

Front

What does it mean for a function to be 'steeper'?

Back

A function is considered 'steeper' when its slope increases, meaning it rises or falls more sharply.

Front

What is the effect of replacing f(x) with 2f(x)?

Back

Replacing f(x) with 2f(x) results in a vertical stretch of the graph by a factor of 2.

Front

How does the equation y = -3f(x) + 5 transform the parent function?

Back

This transformation reflects the graph over the x-axis, makes it steeper, and translates it up by 5 units.

Front

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

Back

A vertical compression reduces the steepness of the graph, making it flatter.