Question

1. a function is

1 point
a) a graph that is a straight line
b) a relationship that goes through the origin
c) a relationship where each input matches to exactly one output
d) a relationship where an input can have multiple outputs

1. does the graph represent a linear or nonlinear function?

1 point
how do you know?

1. mr. nickerson is saving money for a new fishing rod. he has $80 in his bank account and is saving

$20 per month. the situation is modeled by the following function where x is the number of months:
1 point each
$f(x)=20x + 80$
a) find $f(5)$
b) what does $f(5)$ mean in context of the problem?
c) find x if $f(x)=240$
d) if the fishing rod costs $360, how many months will mr. nickerson have to save?

Explanation:

1)

Step1: Recall function definition

A function is a relationship where each input matches to exactly one output. A graph that is a straight line is a linear function (a subset of functions). A relationship through the origin is \(y = kx\) (a type of linear function). A relationship with an input having multiple outputs is not a function.

2)

Step1: Check for linearity

A linear function has a constant rate of change and its graph is a straight line. The given graph is not a straight line. So it is a nonlinear function.

3a)

Step1: Substitute \(x = 5\) into \(f(x)=20x + 80\)

$$
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$$

3b)

Step1: Interpret in context

Since \(x\) is the number of months and \(f(x)\) is the total money saved. \(f(5)\) means the total money Mr. Nickerson has saved after 5 months.

3c)

Step1: Set \(f(x)=240\) and solve for \(x\)

$$
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$$

3d)

Step1: Set \(f(x) = 360\) and solve for \(x\)

$$
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$$

Answer:

1. C. A relationship where each input matches to exactly one output
2. Non - linear function. The graph is not a straight line.

3.
a. \(180\)
b. The total money Mr. Nickerson has saved after 5 months.
c. \(8\)
d. \(14\)