+0

0
435
8

The graph of \$y=f(x)\$ is shown below. Assume \$f(x)\$ is defined only on the domain shown, and that the \$y\$-axis is an axis of symmetry for the graph.

For any real number \$c\$, let \$g(c)\$ be the number of solutions to the equation \$f(x)=c\$. What is the average of all distinct values in the range of \$g(c)\$? Dec 6, 2018

#1
#2
0

Could you please edit your question to get rid of all the irrelevant \$ signs.

Then it will be easier to read and someone might attempt an answer.

Melody  Dec 7, 2018
#3
0

The graph of \(y=f(x)\) is shown below. Assume \(f(x)\) is defined only on the domain shown, and that the \(y\)-axis is an axis of symmetry for the graph.

For any real number \(c\), let \(g(c)\) be the number of solutions to the equation \(f(x) = c\). What is the average of all distinct values in the range of \(g(c)\) Dec 7, 2018
#4
+2

I think questions like this one are always really hard to understand and I would like another mathematician to check my answer.

Use my pic, which is near enough to the same.

Think about a horizontal line through the graph.

At the top it will pass through the graph twice so  g(c)=2

Here is a pic

I have drawn six horizonal lines.

For the top (purple - 1st ) one    f(x)=-2

this crosses the graph f(x) at 2 different x values so  g(-2)=2

the next horizontal line (black 2nd )  palsses through 4 points so  g(-2.8)=4

the 3rd horizontal line (red )  palsses through 6 points so  g(-3.4)=6

the 4th horizontal line (blue )  palsses through 5 points so  g(-4)=5

the 5th horizontal line (green)  palsses through 4 points so  g(-5)=4

the bottom horizontal line (purple )  palsses through 2 points so  g(-6.7)=2

So g(c) can be 2, 4, 5, or 6

The average of the distict values of g(c) = (2+4+5+6)/4 = 17/4 = 4.25

I am pretty sure that is correct.

Here is the graph I used         https://www.desmos.com/calculator/ft9bo78w4l

You do not need it though. Dec 8, 2018
edited by Melody  Dec 8, 2018
#5
+1

Since you wanted another mathematician to check this, I will say that this is how I interpreted the question as well. I believe you got the correct answer, Melody.

TheXSquaredFactor  Dec 8, 2018
#6
0

Thanks x-squared :)

Melody  Dec 9, 2018
#7
0  , sorry but the right answer is 3.4

otaku  Dec 12, 2018
#8
0

Yes I forgot the 0.

No big deal, I showed you how to do it.

You can pick up trivial errors like that on your own.

You do not need to be sorry - I did it correctly.

A thank you would be nice though.

Melody  Dec 12, 2018