Transformations of Linear Functions

The video tutorial explains how to transform the identity function f(x) = x into the function g(x) = 2/3x - 3 using linear transformations. It covers the steps to graph linear functions by first graphing the identity function, then applying vertical compression or stretching, reflection, and vertical shifts. The tutorial demonstrates these transformations with specific values, showing how to graph g(x) by selecting key points, applying transformations, and verifying the slope and intercept.

What is the slope of the function g(x) = 2/3x - 3?

• 2/3

• 1

• 0

• -3

In the function g(x) = 2/3x - 3, what does the -3 represent?

• Slope

• Vertical intercept

• Horizontal intercept

• Reflection

What is the first step in graphing a linear function using transformations?

• Shift the graph

• Reflect the graph

• Find the slope

• Graph the identity function

If the absolute value of the slope m is less than 1, what happens to the graph?

• It is reflected

• It is shifted

• It is compressed

• It is stretched

For the function g(x) = 2/3x - 3, what transformation occurs due to the slope?

• Vertical stretch

• No transformation

• Vertical compression

• Reflection

How many units is the function g(x) = 2/3x - 3 shifted vertically?

• Up 3 units

• Down 3 units

• Up 2 units

• Down 2 units

What is the y-value of the point (3, 3) after vertical compression by a factor of 2/3?

• 3

• 2

• 1

• 0

After compressing the graph by a factor of 2/3, what is the y-value of the point (6, 6)?

• 2

• 3

• 6

• 4

What is the final position of the point (0, 0) after all transformations?

• (0, 0)

• (0, -2)

• (0, -3)

• (0, 3)

How do you verify the slope of the transformed function g(x)?

• Check the reflection

• Check the rise over run

• Check the horizontal intercept

• Check the vertical intercept