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This printable supports Common Core Mathematics Standard HSF-LE.A.2

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# 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 $x$ and the vertical axis $f(x)$.
1. $f(x) = -x$
2. $f(x) = -2x$
3. $f(x) = -1/2 x$
4. $f(x) = 1/2 x$
2.
What is the equation of the linear function pictured below? Assume that the horizontal axis represents $x$ and the vertical axis $f(x)$.
1. $f(x) = 1/2 x$
2. $f(x) = 2x$
3. $f(x) = x$
4. $f(x) = 1/2x + 1$
3.
Some of the values of $f(x)$ are given in the table below. What is the function rule for this linear function?

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

 $\ \ \ \ \ \ \ \ \ \ \ mathbf{x} \ \ \ \ \ \ \ \ \ \ \$ $\ \ \ \ \ \ \ \ \ \ \mathbf{f(x)} \ \ \ \ \ \ \ \ \ \$ $-3$ $-17/2$ $-1$ $-15/2$ $1$ $-13/2$ $3$ $-11/2$
1. $f(x) = 1/2 x - 7$
2. $f(x) = x - 11/2$
3. $f(x) = 2x - 5/2$
4. $f(x) = x - 7$
5.
Create a linear function, given the points $(-2,5)$ and $(1,-2)$.
1. $f(x) = 7/3 x - 13/3$
2. $f(x) = -3/7 x - 11/7$
3. $f(x) = 3/7 x - 17/7$
4. $f(x) = -7/3 x + 1/3$
6.
Create a linear function from the points $(-5,4)$ and $(3,4)$.
1. $f(x) = 4$
2. $f(x) = 1/9 x + 11/3$
3. $f(x) = -1/9 x + 31/9$
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, $M$, Anna will have received from her aunt, in total, given how many years, $y$, have passed since her 9th birthday?
1. $M(y) = 10y$
2. $M(y) = 10y + 10$
3. $M(y) = 10y - 10$
4. $M(y) = y + 10$
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, $f$, depending on the number of hours he spends fishing, $h$?
1. $f(h) = 3h - 5$
2. $f(h) = 5(h-3)$
3. $f(h) = 5h- 3$
4. $f(h) = (5-3)h$
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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