Question

WILL GIVE MEDAL. c:
The equation below shows the perimeter f(x) of several rectangular paintings having width x inches:

f(x) = 40 + 2x

The perimeter of each painting is less than 92 inches. Which of the following best describes the domain of f(x)?
Choices:
All real numbers greater than 0 and less than 26

All real numbers greater than 0 and less than 92

All integers greater than 0 and less than 26

All integers greater than 0 and less than 92

Answer 1

Hint:
Domain in this context means the values of x that will give
1. a positive width
2. a perimeter, f(x) less than or equal to 92.
For example, if x=30, then f(x)=40+2*30=100, so 30 is not in the domain of f(x).
To find the domain, you need to figure out a maximum and minimum value of x so that all values between the two extremes are valid/acceptable.

Answer 2

Can you explain to me how to find the min & max?

Answer 3

What is the minimum width possible?

Answer 4

uhh, dunno .-. i've never done a problem like this and it's the only one on this assignment

Answer 5

How small can width be? Can it be zero? Can it be -1?

Answer 6

0?

Answer 7

Good, except that it cannot be exactly zero, so we say x>0.

Answer 8

Now we know that the perimeter cannot exceed 92.
We know the perimeter is f(x).
so we look for x such that f(x)=92, that would be the maximum.
Can you find that?
f(x)=40+2x=92
Solve for x.

Answer 9

f(x)= 40+2x=92
-40 -40
2x= 52
2x/2= 52/2
x= 26 ?

Answer 10

Great! That's the maximum value x can take to make a perimeter of 92.
But we were told that the perimeter must be less than 92, so what can you say about x?

Answer 11

that x equals 0?

Answer 12

no wait

Answer 13

ugh idk I:

Answer 14

We don't want f(x) to go over 92, so we limit x to be less than 26. Does that make sense?

Answer 15

yes

Answer 16

So now we know that x has to be greater than zero, and less than 26. Can you put the two conditions together in a math expression?

Answer 17

x<0>26?

Answer 18

i think

Answer 19

was i close?

Answer 20

Almost!
0<x<26

Answer 21

This represents the valid values of x for the given problem.
Can you find the math term for this "valid values of x"?

Answer 22

hmm

Answer 23

How about domain!

Answer 24

OH

Answer 25

x is domain and y is range XD i forgot

Answer 26

Now you're ready to go and make your choice of answer! :)

Answer 27

thank you :)

Answer 28

*answers

Answer 29

You're welcome! :)

Answer 30

wait is it integers or all numbers?

Answer 31

@mathmate

Answer 32

Good question.
Since measurements of width are not limited to integers, so x can take any real number withing the extremes.