Constructing Linear Functions (Grade 9)

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Constructing Linear Functions

1. 
What is the equation of the linear function in the graph? Assume the horizontal axis represents [math]x[/math] and the vertical axis [math]f(x)[/math].
Graph - Linear Function y=-2x
  1. [math]f(x) = -x[/math]
  2. [math]f(x) = -2x[/math]
  3. [math]f(x) = -1/2 x[/math]
  4. [math]f(x) = 1/2 x[/math]
2. 
What is the equation of the linear function pictured below? Assume that the horizontal axis represents [math]x[/math] and the vertical axis [math]f(x)[/math].
Graph - Linear Function y=1/2x
  1. [math]f(x) = 1/2 x[/math]
  2. [math]f(x) = 2x [/math]
  3. [math]f(x) = x[/math]
  4. [math]f(x) = 1/2x + 1[/math]
3. 
Some of the values of [math]f(x)[/math] are given in the table below. What is the function rule for this linear function?


[math] \ \ \ \ \ \ \ \ \ \ \ mathbf{x} \ \ \ \ \ \ \ \ \ \ \ [/math][math] \ \ \ \ \ \ \ \ \ \ \mathbf{f(x)} \ \ \ \ \ \ \ \ \ \ [/math]
[math] 0 [/math][math] 2 [/math]
[math] 1 [/math][math] -8 [/math]
[math] 2 [/math][math] -18 [/math]
[math] 3 [/math][math] -28 [/math]
  1. [math]f(x) = 10x - 2[/math]
  2. [math]f(x) = -10x + 2[/math]
  3. [math]f(x) = 10x + 2[/math]
  4. [math]f(x) = -10x - 2[/math]
4. 
The following table shows some of the values for the linear function [math]f(x)[/math]. Find the correct function rule.

[math] \ \ \ \ \ \ \ \ \ \ \ mathbf{x} \ \ \ \ \ \ \ \ \ \ \ [/math][math] \ \ \ \ \ \ \ \ \ \ \mathbf{f(x)} \ \ \ \ \ \ \ \ \ \ [/math]
[math] -3 [/math][math] -17/2 [/math]
[math] -1 [/math][math] -15/2 [/math]
[math] 1 [/math][math] -13/2 [/math]
[math] 3 [/math][math] -11/2 [/math]
  1. [math]f(x) = 1/2 x - 7[/math]
  2. [math]f(x) = x - 11/2[/math]
  3. [math]f(x) = 2x - 5/2[/math]
  4. [math]f(x) = x - 7[/math]
5. 
Create a linear function, given the points [math](-2,5)[/math] and [math](1,-2)[/math].
  1. [math]f(x) = 7/3 x - 13/3[/math]
  2. [math]f(x) = -3/7 x - 11/7[/math]
  3. [math]f(x) = 3/7 x - 17/7[/math]
  4. [math]f(x) = -7/3 x + 1/3[/math]
6. 
Create a linear function from the points [math](-5,4)[/math] and [math](3,4)[/math].
  1. [math]f(x) = 4[/math]
  2. [math]f(x) = 1/9 x + 11/3[/math]
  3. [math]f(x) = -1/9 x + 31/9[/math]
  4. The line that these points define is not a function.
7. 
Anna is 9 years old, and this year she received $10 from her aunt on her birthday. Her aunt has told her that she will send $10 every birthday from now on. Which function best describes how much money, [math]M[/math], Anna will have received from her aunt, in total, given how many years, [math]y[/math], have passed since her 9th birthday?
  1. [math]M(y) = 10y[/math]
  2. [math]M(y) = 10y + 10[/math]
  3. [math]M(y) = 10y - 10[/math]
  4. [math]M(y) = y + 10[/math]
8. 
Max usually goes fishing when he's on vacation. He spends at least an hour out on the ocean when he goes fishing, and usually catches 5 fish per hour. However, on the way home, seagulls usually eat about 3 of the fish he has caught. Which of the following functions best describes how many fish Max brings home on a given day, [math]f[/math], depending on the number of hours he spends fishing, [math]h[/math]?
  1. [math]f(h) = 3h - 5[/math]
  2. [math]f(h) = 5(h-3)[/math]
  3. [math]f(h) = 5h- 3[/math]
  4. [math]f(h) = (5-3)h[/math]
9. 
A plumber charges $25 for a service call plus $50 per hour of service. What will be the total cost for 8 hours of work?
  1. $400
  2. $83
  3. $425
  4. $75
10. 
The cost of a gallon of gasoline, g, is $3.25 less than 2 times the cost of a gallon of diesel, d. If a gallon of gasoline costs $3.95, what is the cost of a gallon of diesel?
  1. $3.60
  2. $4.00
  3. $3.68
  4. $4.35

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