Question

values of a house in january in denver, colorado, for different years are as follows: 2014, $254,000; 2015, $293,000; 2016, $338,000; 2017, $372,000.
a. make a table.
b. determine the domain and range of the relation.
c. determine whether the relation is a function.

examples 4 and 5
if $f(x) = 3x + 2$ and $g(x) = x^2 - x$, find each value.

1. $f(4)$
2. $f(8)$
3. $f(-2)$
4. $g(2)$
5. $g(-3)$
6. $g(-6)$
7. $f(2) + 1$
8. $f(1) - 1$
9. $g(2) - 2$
10. $g(-1) + 4$
11. $f(x) + 1$
12. $g(3b)$

example 6

1. cell phones many cell phone plans have an option to include more than one phone. the function for the monthly cost of cell phone service from a wireless company is $f(x) = 25x + 200$, where x is the number of phones on the plan, and interpret $f(3)$ and $f(5)$.
2. geometry the area for any square is given by the function $f(x) = x^2$, wh... find and interpret $f(3.5)$.

Explanation:

Step1: Substitute x=4 into f(x)

$f(4) = 3(4) + 2$

Step2: Calculate f(4)

$f(4) = 12 + 2 = 14$

Step1: Substitute x=-3 into g(x)

$g(-3) = (-3)^2 - (-3)$

Step2: Calculate g(-3)

$g(-3) = 9 + 3 = 12$

Step1: Substitute x=2 into f(x), add 1

$f(2)+1 = [3(2)+2] + 1$

Step2: Calculate f(2)+1

$f(2)+1 = (6+2)+1 = 8+1=9$

Step1: Substitute x=2 into g(x), subtract 2

$g(2)-2 = [(2)^2 - 2] - 2$

Step2: Calculate g(2)-2

$g(2)-2 = (4-2)-2 = 2-2=0$

Step1: Substitute x=-1 into g(x), add 4

$g(-1)+4 = [(-1)^2 - (-1)] + 4$

Step2: Calculate g(-1)+4

$g(-1)+4 = (1+1)+4=2+4=6$

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For the house value relation:

a. The table organizes years (input) and corresponding house values (output).
b. Domain is all input values (years); range is all output values (house prices).
c. A relation is a function if each input maps to exactly one output.

Step1: Substitute x=3 into f(x)

$f(3) = 25(3) + 200$

Step2: Calculate f(3)

$f(3) = 75 + 200 = 275$
Interpretation: The monthly cost for 3 phones on the plan is $275.

Step1: Substitute x=5 into f(x)

$f(5) = 25(5) + 200$

Step2: Calculate f(5)

$f(5) = 125 + 200 = 325$
Interpretation: The monthly cost for 5 phones on the plan is $325.

Answer:

a.

Year	House Value
2015	$293,000
2016	$338,000
2017	$372,000

b. Domain: {2014, 2015, 2016, 2017}
Range: {$254,000, $293,000, $338,000, $372,000}

c. Yes, the relation is a function.

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For the cell phone function: