## anonymous one year ago Based on the graph below, what are the solutions to the equation f(x) = g(x)?

1. anonymous

x = -3, 0.8, 4 x = -1.9, 0.8, 4.1 x = -2, 2, 3 x = -2.5, 0.8, 3 Those are the options and then the graph is attached

2. Michele_Laino

from your graph we have three intersection points

3. anonymous

Yes, I get it, however none of the answers match and I'm really confused because I thought it just was where the two lines connect in those 3 points but that doesn't match any of my options

4. Michele_Laino

I think that we can choose the first option

5. Michele_Laino

it is the one closest to the right result

6. anonymous

yeah, I really hope your right haha thanks

7. Michele_Laino

:)

8. anonymous

Wait do you have time to help me with another one?

9. Michele_Laino

yes!

10. anonymous

THANK YOU

11. anonymous

Water coming out from a fountain is modeled by the function f(x) = -x2 + 6x + 6 where f(x) represents the height, in feet, of the water from the fountain at different times x, in seconds. What does the average rate of change of f(x) from x = 2 to x = 5 represent? (4 points) The water travels an average distance of 4 feet from 2 seconds to 5 seconds. The water travels an average distance of 1 foot from 2 seconds to 5 seconds. The water falls down with an average speed of 2 feet per second from 2 seconds to 5 seconds. The water falls down with an average speed of 1 foot per second from 2 seconds to 5 seconds.

12. Michele_Laino

we have to compute the average rate, using this formula: $\Large r = \frac{{f\left( 5 \right) - f\left( 2 \right)}}{{5 - 2}}$

13. Michele_Laino

where: $\Large \begin{gathered} f\left( 5 \right) = - {5^2} + 6 \cdot 5 + 6 = ... \hfill \\ f\left( 2 \right) = - {2^2} + 6 \cdot 2 + 6 = ... \hfill \\ \end{gathered}$

14. anonymous

f(5) = 11 f(2) = 14

15. Michele_Laino

ok! so after a substitution, we get: $\Large r = \frac{{f\left( 5 \right) - f\left( 2 \right)}}{{5 - 2}} = \frac{{11 - 14}}{{5 - 2}} = ...$

16. anonymous

-4 ---- 3

17. Michele_Laino

11-14=-3

18. anonymous

whoops hehe sorry

19. Michele_Laino

:) so r= -1, right?

20. anonymous

yeah

21. Michele_Laino

now since f(5)= 11 and f(2) = 14, we can say that going from 2 seconds to 5 seconds water is falling down

22. anonymous

at 3 feet per second?

23. anonymous

sorry 1 foot per second

24. Michele_Laino

so, what is the right option?

25. anonymous

4 or 2

26. anonymous

4

27. Michele_Laino

please keep in mind that water is falling down with a rate equal to 1 (if we neglect the minus sign)

28. Michele_Laino

correct!

29. anonymous

Thank you so much, you are really helpful!

30. Michele_Laino

:) :)