Question

The table below shows the square roots of different numbers:

Number
(x) 4 4 9 9
Square root
(y) 2 -2 3 -3

Part A: Does the table represent y as a function of x? Justify your answer. (5 points)

Part B: The total cost f(x), in dollars, for renting a car for a week and driving it x miles is shown below:

f(x) = 90 + 0.11x

What is the value of f(300), and what does f(300) represent? (5 points)

Answer 1

it is not a function because there is repeating x values. A function can have repeating y values, just not the x ones.

f(x) = 90 + 0.11x....f(300)
f(300) = 90 + 0.11(300)
f(300) = 90 + 33
f(300) = 123

f(300) represents the 300 miles u drive...and its cost is $ 123

Answer 2

a.No, given table does not represent y as function of x.

b.f(300)=123 miles

f(300) represent the total cost of car for driving 300 miles.

Explanation:

We are given that

Number (x) 4 4 9 9

Square root(y) 2 -2 3 3

a.We have to find that given table represent y as function of x.

We know that function is mapping between two non- empty set A and B .

Every element in set A has a unique image in set B.

One element in set A can not have more than one image in set B

But two or more than elements in set A can have same images in set B.

But from given table

Image of 4 are 2 and -2 which is not possible by definition of function.

Hence, tables does not represent y as a function of x.

B.
`f(x)=90+0.11 x`

Where f(x)= Total cost (in dollars) for renting a car for a week

x=Driving distance (miles)

Substitute x=300

Then, we get
`f(300)=90+0.11(300)=90+33=123 miles`

Hence, f(300) represent the total cost of rent of car for driving 300 miles .