Transformations of Linear Functions

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.

Front

What does the slope of a linear function represent?

Back

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

Front

What is the parent function of linear functions?

Back

The parent function of linear functions is f(x) = x, which is a straight line passing through the origin with a slope of 1.

Front

How does the equation y = mx + b affect the graph of a linear function?

Back

The value of m affects the steepness and direction of the line, while b determines the point where the line crosses the y-axis.

Front

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

Back

A vertical translation shifts the graph of the function up or down without changing its shape. For example, f(x) = x + 3 shifts the graph up 3 units.

Front

What is a horizontal translation in the context of linear functions?

Back

A horizontal translation shifts the graph of the function left or right. For example, f(x) = x - 2 shifts the graph right 2 units.

Front

What does a vertical stretch of a linear function do?

Back

A vertical stretch increases the steepness of the line. For example, f(x) = 2x is a vertical stretch of the parent function f(x) = x.

Front

What does a horizontal compression of a linear function do?

Back

A horizontal compression makes the graph steeper by reducing the width of the graph. For example, f(x) = 3x compresses the graph horizontally.

Front

How does the equation y = 3f(x) - 2 transform the parent function?

Back

This equation represents a vertical stretch by a factor of 3 and a vertical translation down 2 units.

Front

What is the effect of changing the sign of the slope in a linear function?

Back

Changing the sign of the slope reflects the graph across the x-axis. For example, f(x) = -x is a reflection of f(x) = x.