(04.07) julie is at the store buying groceries. she needs to get a quart of orange juice and some peaches. the quart of orange juice costs $2.25 and the peaches are $0.75 each. the function f(x) = 0.75x + 2.25 represents julie's expenses at the grocery store. what do the f(x) and the x represent?

f(x) is the total cost and x is the number of peaches.

Step-by-step explanation:

We know that each peach costs $0.75.  This means the expression 0.75x represents the total cost of peaches; this makes x represent the number of peaches.

We also know that $2.25 is the cost of juice.  Adding it to the cost of peaches gives us the total cost; this means f(x) represents the total cost.

7. d. 64

8. i. 32

9. c. 125

10. j. none of the above

11. d. 81

12. i. 216

13. e. none of the above

14. g. 240

15. e. none of the above

16. g. 32

17.   e. none of the above

1 number

if we use a graphing calculator, there is only one such number that satisfies the conclusion of the mean value theorem, that is, a number such that

where the right-hand side is the average rate of change of f on the interval [0.5,0.75], which is the slope of the secant line.

in the attached graph, the black line is the secant line which has its slope as the average rate of change of f on [0.5,0.75], while the orange line is the only tangent line to the graph of f in the interval that satisfies the mvt conclusion.