Module 5: Relationships Among Linear Functions - Review

Module 5: Relationships Among Linear Functions

5.2 - Transform Linear Functions

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  • Class Notes Folder

  • Module 1 Review Matrix - Document

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5.4 - Inverses of Linear Functions

5.1 - Transform Graphs of Functions

5.3 - Compare Linear Functions

Class Notes Algebra 1B 24-25 T2 - Google Drive

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Domain, Input, x's


Range
Output
y's

5.1 and 5.2 - Transform
Linear Functions

Multiple Choice

What is the parent linear functions?

• y = 2x

• y = mx + b

• f(x) = x

• Not here

Multiple Choice

The linear parent function, f(x) = x, is transformed to g(x) = -6f(x). Describe the transformation.

• g(x) is reflected over the x-axis and stretched vertically by a factor of 6

• g(x) is shifted down 6 units

• g(x) is shifted left 6 units

• g(x) is reflected over the x-axis and stretched horizontally by a factor of 6

Multiple Choice

Use the graphs of f and g to describe the transformation from the graph of f to the graph of g.

• The graph of g is a vertical translation 2 units up of the graph of f
• The graph of f is a horizontal translation two units left of g
• The graph of g is a vertical stretch by a factor of 2 of the graph of f
• The graph of g is a reflection of the graph of f

Multiple Choice

Which represents the parent function shifted down two units?

• f(x) = -2x

• f(x) = x - 2

• f(x) = x + 2

• f(x) = 2x

Multiple Choice

The linear parent function, f(x) = x, is transformed to g(x) = f(x) - 6. Describe the transformation.

• g(x) is shifted up 6 units

• g(x) is shifted down 6 units

• g(x) is shifted left 6 units

• g(x) is shifted right 6 units

Multiple Choice

The linear parent function, f(x) = x, is transformed to g(x) = f(x) + 3. Describe the transformation.

• g(x) is shifted up 3 units

• g(x) is shifted down 3 units

• g(x) is shifted left 3 units

• g(x) is shifted right 3 units

Features of Linear Functions:
y-intercept (b)
slope (m)
zero of a function (x-intercept)

5.3 -
Compare Linear Functions

Multiple Choice

Write a linear equation in the form of y=mx+b

• y = 2x + 2

• y = 2x - 2

• y = x + 2

• y = 3x - 2

Multiple Choice

Write a linear equation in the form of y=mx+b

• y = 3x - 3

• y = -3x + 3

• y = -3x - 3

• y = 3x + 3

Multiple Choice

What is the equation of the linear function?

• y= x -12

• y= x + 12

• y= -x + 12

• y= -x - 12

Open Ended

Equation A: y = 2x + 3

Equation B: y = 3x - 3

Which equation has a higher slope?

Open Ended

Equation A: y = 3x - 1

Equation B: y = 1/2x + 1

Which equation has a higher y-intercept?

Open Ended

Compare the rates of change. Do they have the same rate of change? If they have different rates of change, which one is greater?

Open Ended

The cost of Nate’s service is described by y = 4x + 6. The table shows the cost of Beth’s service. Find the equation for Beth's service. Which service is cheaper for 8 movies in one month?

The inverse of a function is a function that has had it's domain and range switched.

5.4 -
Inverses of Linear Functions

Reorder

Given the function f(x)= 2x-5, put the work in the correct order to find the inverse function.

• $$y=2x-5$$

• $$y+5=2x$$

• $$\frac{y+5}{2}=x$$  

• $$\frac{x+5}{2}=y$$

• $$f^{-1}\left(x\right)=\frac{x+5}{2}$$

1

2

3

4

5

• 1
• 2
• 3
• 4
• 5

Multiple Choice

Find the inverse of $$f\left(x\right)=3x+2$$  

• $$f^{-1}\left(x\right)=\frac{x-2}{3}$$  

• $$f^{-1}\left(x\right)=\frac{x-3}{2}$$  

• $$f^{-1}\left(x\right)=\frac{3x}{2}$$  

• $$f^{-1}\left(x\right)=\frac{2+x}{3}$$  

Multiple Choice

Find the inverse of  $$f(x)=10+7x$$  

• $$f^{-1}(x)=\frac{x-7}{10}$$

• $$f^{-1}(x)=\frac{x-10}{7}$$

• $$f^{-1}(x)=\frac{1}{10+7x}$$

Multiple Choice

What is the inverse of the function
f(x) = 2x + 4   ?

• f^-1(x) = 4(x -2)
• f^-1(x) = (x-4)/2
• f^-1(x) = x/2 - 4
• f^-1(x) = x/4 + 2