Transformation of Linear Function

Front

What is a linear function?

Back

A linear function is a function that can be graphically represented as a straight line. It has the form f(x) = mx + b, where m is the slope and b is the y-intercept.

Tags

CCSS.8.F.B.4

CCSS.HSF.LE.A.2

Front

What does the slope of a linear function represent?

Back

The slope of a linear function represents the rate of change of the function. It indicates how much the y-value changes for a unit change in the x-value.

Tags

CCSS.8.EE.B.5

Front

What is the y-intercept of a linear function?

Back

The y-intercept is the point where the graph of the function crosses the y-axis. It is represented by the value of b in the function f(x) = mx + b.

Front

How does a transformation affect the graph of a linear function?

Back

A transformation can change the position, shape, or size of the graph. Common transformations include translations, reflections, stretches, and compressions.

Front

What is a vertical translation of a linear function?

Back

A vertical translation shifts the graph of the function up or down. For example, f(x) + k translates the graph up by k units if k > 0 and down if k < 0.

Front

What is a horizontal translation of a linear function?

Back

A horizontal translation shifts the graph of the function left or right. For example, f(x - h) translates the graph right by h units if h > 0 and left if h < 0.

Front

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

Back

A linear function is considered 'steeper' if it has a larger absolute value of the slope (m). A steeper slope means the line rises or falls more sharply.

Front

What is a reflection in the context of linear functions?

Back

A reflection flips the graph of the function over a specific line, such as the x-axis or y-axis. For example, f(x) reflected over the x-axis is -f(x).

Front

What is a vertical stretch of a linear function?

Back

A vertical stretch occurs when the slope of the function is multiplied by a factor greater than 1. For example, g(x) = 2f(x) stretches the graph vertically.

Front

What is a vertical compression of a linear function?

Back

A vertical compression occurs when the slope of the function is multiplied by a factor between 0 and 1. For example, g(x) = 1/2f(x) compresses the graph vertically.