Question

Your friend has $100 when he goes to the fair. He spends $10 to enter the fair and $20 on food. Rides at the fair cost $2.00 per ride. Which function can be used to determine how much money he has left over after x rides?

A. f(x) = -2x + 70

B. f(x) = 2x + 70

C. f(x) = -2x - 70

D. f(x) = -30x + $100


A student is running a 5-kilometer race. He runs 1 kilometer every 3 minutes. Select the function that describes his distance from the finish line.

A. f(x) = - 1 over 3 x + 5

B. f(x) = - 1 over 5 x + 3

C. f(x) = 1 over 5 x + 5

D. f(x) = 1 over 3 x + 3

Answer 1

So, we first take the deduction from the initial $100. Deducting 20 and 10 respectively, we're left with $70. Now, the $2 is going to have a subtraction effect on the remaining $70. Our answer is: x tickets times -2 + the $70 he had before the rides! Or option A.

The second question is a bit more nuanced. For every increase in x you're going to increase the fraction. We know that after 3 minutes he has run 1 out of the 5 miles. So it will take him 15 minutes to run the full 5 miles, where 15 is equal to x if it's a function. 15 * 1/3 = 5. We want it to get closer and closer to 0, because we're looking at the distance TO the finish line, so by making the number added to the 5 kilometers negative it gets closer and closer to zero. Our answer is: -1/3 * x + 5, or option A.

Answer 2

Thank you so much!! you have no idea how much i appreciate this, can you help me with 2 more questions?


1.)A science experiment begins with a metal at -100° Celsius. The following function describes the temperature change per minute: f(x) = 89x - 100°. How will the graph of this function change if the metal is at 25° at the start of the experiment?

The line will shift vertically up by 125°.

The line will shift vertically up by 25°.

The line will shift vertically down by 125°.

The line will shift vertically down by 25°.

2.)You attend an amusement park with your family. Your parents buy you an all-ride pass for $20, shown as f(x). Instead of getting a pass, your parents decide to pay $4.00 for each ride they take, shown as g(x). What function shows the correct combination of these two functions to represent the total cost to them of attending the amusement park that day, shown as h(x)?

f(x) = 20x, g(x) = 4, h(x) = 20x + 4

f(x) = 20, g(x) = 4, h(x) = 4 + 20

f(x) = 20, g(x) = 4x, h(x) = 4x + 20

f(x) = 20x, g(x) = 4x, h(x) = 20x + 4x

Answer 3

I'm afraid I don't understand the first question.

The second question is much like the first one, and functions begin to make more sense the more you do them. Let's look at it real quick.

So, f(x) is a one time purchase and is equivalent to 20 dollars. We know that they don't intend to purchase another one of these all day passes due to the wording of the problem, so we can conclude that it is 20 and will always be 20. For g(x) there is some unknown variable that will affect the number of times the parents spend their 4 dollars, that being the number of times they choose to ride the amusement park's rides. Since we don't know that let's just call it x, so we have 4x. We want to know the total, and so we take the sum of those two functions to make our final function, h(x) = 4x +20, or option C.

Good luck with your other one, sorry I couldn't help!

Answer 4

It takes a total of 6 hours to fill up an in ground backyard pool using a standard hose. A function can represent this situation to represent the amount of water in the pool until it is full as a function of the time the hose is running. Determine the domain for this function.

The domain is all integers from 0 to 6 hours.

The domain is all even integers from 0 to 6 hours.

The domain is all real numbers from 0 to 6 hours.

The domain is all positive real numbers.

Answer 5

Thank you so much econ.ruiz! you have helped so muchhh

Answer 6

No problem, this is good practice.

The domain is your x value in a function. So, if we were to make a function out of this we might use the hours that it takes to fill the pool to represent the x, right? So, it can't be D because that includes numbers that aren't 0-6. Can't be B because that's just the even ones. We're left with A or C, and it comes down to whether or not it should be integers or real numbers... and I'm gonna guess they want real numbers, because that means we can include rational numbers (fractions, decimals, roots, etc).

So, our answer is C.