Linear Function Transformations

Front

What is a linear function?

Back

A linear function is a function that graphs to a straight line, represented by the equation f(x) = mx + b, where m is the slope and b is the y-intercept.

Front

What does it mean to transform a function?

Back

To transform a function means to change its position, size, or shape on a graph.

Front

What is a reflection in terms of function transformations?

Back

A reflection is a transformation that flips a graph over a line, such as the x-axis or y-axis.

Front

What is a translation in function transformations?

Back

A translation is a transformation that shifts a graph horizontally or vertically without changing its shape.

Front

What does it mean for a graph to be steeper?

Back

A graph is steeper when its slope (m) is greater, indicating that it rises or falls more sharply.

Front

What does it mean for a graph to be less steep?

Back

A graph is less steep when its slope (m) is smaller, indicating a gentler rise or fall.

Front

How do you translate a function up by 3 units?

Back

To translate a function up by 3 units, you add 3 to the output: f(x) becomes f(x) + 3.

Front

How do you double the slope of a linear function?

Back

To double the slope of a linear function, multiply the slope (m) by 2 in the equation f(x) = mx + b.

Front

What is the parent function of a linear equation?

Back

The parent function of a linear equation is f(x) = x, which is the simplest form of a linear function.

Front

What happens to the graph of f(x) = 2x - 1 when translated down 2 units?

Back

The new function becomes f(x) = 2x - 3.