Question

17. MODELING WITH MATHEMATICS The function
25x + 500 represents your monthly rent y
(in dollars) when you pay x days late,

a. Identify the independent and dependent variables?
b.the domain is 0,1,2,3,4 and 5. what is the range?

Answer 1

Using function concepts, it is found that:

a) x is the independent variable and y is the dependent variable.

b) The range is: {500, 525, 550, 575, 600, 625}.

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The function is:

$y = 25x + 500$

Item a:

The value of y is dependent of the value of x, thus, x is the independent variable and y is the dependent variable.

Item b:

• The domain of a function is the set that contains all possible input values.
• The range is the set that contains all possible output values.

• The domain is: {0,1,2,3,4,5}.
• Thus, the range will be the values of y for these values of x.

$y(0) = 25(0) + 500 = 500$

$y(1) = 25(1) + 500 = 525$

$y(2) = 25(2) + 500 = 550$

$y(3) = 25(3) + 500 = 575$

$y(4) = 25(4) + 500 = 600$

$y(5) = 25(5) + 500 = 625$.

Thus, the range is: {500, 525, 550, 575, 600, 625}.

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