Tony plans to run a 5,000-meter fun run at a constant rate of 250 meters per minute. he uses function f to model his distance from the finish line x minutes after the start of the race.

x f(x)
0 5,000
1 4,750
2 4,500
3 4,250
4 4,000
5 3,750
6 3,500

a.
tony's function is always decreasing.
b.
tony's function is always negative.
c.
tony's function is exponential.
d.
the domain of tony's function is [0 , 5,000].

Option A.

Step-by-step explanation:

Based on the information provided on the question

the function used to model Tony's run is:

f(x) = -250*x  + 5000

This means that after x = 20 minutes, Tony will arrive to the finish line

f(20) = -250*(20)  + 5000 = -5000 + 5000 = 0

The function is always decreasing, because we are dealing with a line with negative slope.

Option A.

2

step-by-step explanation:

let's cover over the formula of the vertex:

y = a(x – h)^2 + k

in this formula, (h,k) are the vertex, always remember that the positive or negative value of the vertex is based on the sign it has.

for example, if the vertex is -3,-6 then both the x and y value would have the positive sign attached to it and if it were a positive x and y value, then a negative sign would be attached to it.

with that being said, for our problem the x value is a positive one so we are looking for a number with a negative sign next to it, in this case the first and second choice.

however, for the first answer choice it isn't quite part of the formula so we know that the answer choice correctly displays the x value.

to confirm, we can see if the -1 fits correctly with the second answer choice, and as mentioned above a negative number will have a positive sign attached to it. so, for our problem we can see that -1 has been changed to +1, so we can confirm that the second answer choice is correct.

hence, our final answer is y=(x - 1)^2 + 1