Algebra 3-3 Linear Function Transformations: Shifts, Stretches, and Reflections

What is the parent function for linear transformations?

y = x

What form do we study for changes to lines in this lesson?

y = mx + b

What type of change does Avery's transformation g(x) = (2x + 1) + 2 represent?

A vertical change (output change)

What type of change does Cindy's transformation g(x) = 2(x + 1) + 1 represent?

A horizontal change (input change)

What is the main idea regarding changes to output in linear functions?

Changes to output affect the entire function vertically.

What is the main idea regarding changes to input in linear functions?

Changes to input affect only the 'x' value horizontally.

What tool is suggested for exploring transformations of linear functions?

Desmos Calculator

What is a sequence in the context of linear functions?

A sequence is a list of numbers following a specific pattern.

How do transformations work on different functions?

Transformations work the same on all functions.

What does a linear sequence look like?

A linear sequence has a constant difference between consecutive terms.

What is the effect of a vertical stretch on the graph of a linear function?

It makes the graph steeper.

What does a horizontal shift to the left indicate in a linear function?

It indicates that the input value is decreased.

What does a vertical shift upwards indicate in a linear function?

It indicates that the output value is increased.

What happens to the graph when a negative coefficient is applied to 'x' in a linear function?

The graph reflects over the y-axis.

What is the significance of the 'b' in the equation y = mx + b?

'b' represents the y-intercept of the line.

What does the slope 'm' in the equation y = mx + b indicate?

The slope 'm' indicates the steepness and direction of the line.

What is the result of applying a transformation that includes both vertical and horizontal changes?

The graph will shift both up/down and left/right simultaneously.

What is the relationship between input and output in linear transformations?

Input corresponds to 'x' and output corresponds to 'y'.

What is the first step in analyzing transformations of linear functions?

Identify the parent function and the type of transformation applied.

What does the term 'reflection' mean in the context of linear functions?

Reflection means flipping the graph over a specified axis.