A1-U5.1 Lesson: Linear Transformations

Unit 5 Lesson 1:
Linear Transformations

Objective:

Students are going to identify and perform transformations on linear functions.

Subtract from x.

​Down or Right

Add to x.

Up or Left

Rules: Shifts

Replace x with -x.

Across x-axis:

Multiply by -1.

Across y-axis:

Rules: Reflections

Replace the slope with its reciprocal opposite.

Perpendicular:

Multiply x by a scalar.

Rotations:

Rules: Rotations

Parent function: f(x) = x is graphed in red.

Rule:


g(x) =

​

​Example 1:

Parent function: f(x) = x is graphed in red.

Rule:


g(x) =

​

​Example 2:

Parent function: f(x) = x is graphed in red.

Rule:


g(x) =

​

​Example 3:

Parent function: f(x) = x is graphed in red.

Rule:

​ g(x) =

​Example 4:

Parent function: f(x) = x is graphed in red.

Rule: Shift down 7 units. Graphed in blue.

g(x) = x - 7

​

​Example 1:

Parent function: f(x) = x is graphed in red.

Rule: Shift left 9 units. Graphed in blue.

g(x) = x + 9

​

​Example 2:

Parent function: f(x) = x is graphed in red.

Rule: Reflect across y-axis.

g(x) = -x

​

​Example 3:

Parent function: f(x) = x is graphed in red.

Rule: Increase steepness by a factor of 3 is graphed in blue.

​ g(x) = 3x

​Example 4: