Based on the graph below, what are the solutions to the equation f(x) = g(x)?

- anonymous

Based on the graph below, what are the solutions to the equation f(x) = g(x)?

- jamiebookeater

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- 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

##### 1 Attachment

- Michele_Laino

from your graph we have three intersection points

- 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

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## More answers

- Michele_Laino

I think that we can choose the first option

- Michele_Laino

it is the one closest to the right result

- anonymous

yeah, I really hope your right haha thanks

- Michele_Laino

:)

- anonymous

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

- Michele_Laino

yes!

- anonymous

THANK YOU

- 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.

- Michele_Laino

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

- Michele_Laino

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

- anonymous

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

- Michele_Laino

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

- anonymous

-4
----
3

- Michele_Laino

11-14=-3

- anonymous

whoops hehe sorry

- Michele_Laino

:) so r= -1, right?

- anonymous

yeah

- 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

- anonymous

at 3 feet per second?

- anonymous

sorry 1 foot per second

- Michele_Laino

so, what is the right option?

- anonymous

4 or 2

- anonymous

4

- Michele_Laino

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

- Michele_Laino

correct!

- anonymous

Thank you so much, you are really helpful!

- Michele_Laino

:) :)

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