Which of the following functions has a rate of change of 5? (1 point)
O f (2) = 317 and f (5) = 296
0 f (5) = 300 and f (7) = 290
sf5
ー 225 and f(10) = 250
0 f(3)
278 and f (5)
320
Based on the given information, the function that has a rate of change of 5 is:
- f(2) = 317 and f(5) = 296
To find the function with a rate of change of 5, we need to calculate the slope between two points for each function.
For the first function:
f(2) = 317 and f(5) = 296
The slope can be calculated using the formula:
slope = (change in y) / (change in x)
slope = (296 - 317) / (5 - 2)
slope = -21 / 3
slope = -7
The rate of change for this function is -7, not 5.
For the second function:
f(5) = 300 and f(7) = 290
The slope can be calculated using the formula:
slope = (change in y) / (change in x)
slope = (290 - 300) / (7 - 5)
slope = -10 / 2
slope = -5
The rate of change for this function is -5, not 5.
For the third function:
f(5) = 225 and f(10) = 250
The slope can be calculated using the formula:
slope = (change in y) / (change in x)
slope = (250 - 225) / (10 - 5)
slope = 25 / 5
slope = 5
The rate of change for this function is 5.
For the fourth function:
f(3) = 278 and f(5) = 320
The slope can be calculated using the formula:
slope = (change in y) / (change in x)
slope = (320 - 278) / (5 - 3)
slope = 42 / 2
slope = 21
The rate of change for this function is 21, not 5.
Therefore, the function with a rate of change of 5 is the third function:
f(x) = 5x + 200.
To determine which function has a rate of change of 5, we need to calculate the slope between two points on each function and see if it equals 5.
For the first function, we have f(2) = 317 and f(5) = 296. The slope between these two points can be calculated using the formula: slope = (change in y)/(change in x) = (296-317)/(5-2) = -21/3 = -7. Thus, the rate of change for this function is not 5.
For the second function, we have f(5) = 300 and f(7) = 290. The slope between these two points is (290-300)/(7-5) = -10/2 = -5. The rate of change for this function is 5, so this function has a rate of change of 5.
For the third function, we have f(5) = 225 and f(10) = 250. The slope between these two points is (250-225)/(10-5) = 25/5 = 5. The rate of change for this function is 5.
For the fourth function, we have f(3) = 278 and f(5) = 320. The slope between these two points is (320-278)/(5-3) = 42/2 = 21. Thus, the rate of change for this function is not 5.
Therefore, the functions that have a rate of change of 5 are the second function (f(x) = 300 for x = 5, f(x) = 290 for x = 7) and the third function (f(x) = 225 for x = 5, f(x) = 250 for x = 10).