Solve the problem, If f(x)= x-3A/3x+5 and f(3)=6. what is the value of A?

- anonymous

Solve the problem, If f(x)= x-3A/3x+5 and f(3)=6. what is the value of A?

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- anonymous

@jim_thompson5910

- jim_thompson5910

this is f(x), right?
\[\Large f(x) = \frac{x-3A}{3x+5}\]

- anonymous

Correct

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## More answers

- jim_thompson5910

\[\Large f(x) = \frac{x-3A}{3x+5}\]
\[\Large f(3) = \frac{3-3A}{3(3)+5}\]
\[\Large 6 = \frac{3-3A}{3(3)+5}\]
\[\Large 6 = \frac{3-3A}{14}\]
\[\Large 14*6 = 14*\frac{3-3A}{14}\]
\[\Large 84 = 3-3A\]
\[\Large A = ??\]

- jim_thompson5910

In step 2, I replaced every x with 3
In step 3, I replaced f(3) with 6 (since f(3) = 6)

- anonymous

Okay so I got A= -27

- anonymous

|dw:1433980377815:dw|

- anonymous

Use the accompanying graph of y=f(x) to sketch the graph of the indicated equation.
Graph one transformation in each coordinate system.

- anonymous

@jim_thompson5910

- jim_thompson5910

f(-x) means you reflect over the y axis
2*f(-x) means you scale vertically, or stretch vertically, by a factor of 2

- anonymous

How would I show this on the coordinate plane?

- jim_thompson5910

start by reflecting each point over the y axis

- anonymous

so it would be (-2,-2) and then? what?

- jim_thompson5910

do the same for the other points as well

- jim_thompson5910

|dw:1433981229533:dw|

- jim_thompson5910

|dw:1433981248199:dw|

- jim_thompson5910

imagine this happens to all of the points

- jim_thompson5910

you'd get something like this
|dw:1433981278828:dw|

- anonymous

Okay :)

- anonymous

and then? how would I do the second part?

- jim_thompson5910

the 2* out front means you double each y coordinate

- jim_thompson5910

ex: (2,-2) ----> (2,-4)

- jim_thompson5910

ex: (2,-2) ----> (2,-4)
|dw:1433981434340:dw|
imagine this happens to EVERY point

- anonymous

so I would show this for each point!

- jim_thompson5910

yes

- jim_thompson5910

and the overall graph

- anonymous

Alright awesome thank you!

- anonymous

ONe quick question

- anonymous

Before you leave! :)

- anonymous

If they ask me for which of the following values of x does f(x)=-20
and the graph is showing :|dw:1433981600730:dw|

- jim_thompson5910

draw a horizontal line through y = -20
|dw:1433981843252:dw|

- jim_thompson5910

then determine where that horizontal line crosses the curve

- anonymous

(-25,15), (-15,0), (0,-15) , (10,-20) , (15,-10), (20,10) and (25,0)

- anonymous

those are the points they provide!

- anonymous

I know that -20 and 10 both have f(x)=-20

- jim_thompson5910

hint: y = f(x)

- anonymous

How would I determine the answer?

- anonymous

@jim_thompson5910

- jim_thompson5910

another hint: each point is of the form (x,y)

- anonymous

Would I say {-20,10}

- anonymous

This is all I could think of!

- jim_thompson5910

(-20,10) means x = -20

- jim_thompson5910

but they say f(x) = -20

- anonymous

OKAY,,,, maybe I put it wrong? (-20,-20) and (10,-20)

- jim_thompson5910

just look through the points
(-25,15), (-15,0), (0,-15) , (10,-20) , (15,-10), (20,10) and (25,0)
where the y coord is -20

- jim_thompson5910

y = f(x)
f(x) = -20
y = -20

- anonymous

Okay so all I would say is (10,-20) correct?

- anonymous

@jim_thompson5910

- jim_thompson5910

yes that is the only point that fits the description

- anonymous

okay... and sorry one last thing I PROMISE!!!

- anonymous

iF I HAVE THE SAME coordinate plane but with different points and it is 20 instead of 25 and they ask for what numbers x is f(x)<0?

- anonymous

How would I write this?

- anonymous

It starts with -12 I know this but would it be [-12,-1]

- anonymous

@jim_thompson5910

- jim_thompson5910

can you post a screenshot of the full problem?

- anonymous

|dw:1433982828860:dw|

- anonymous

The graph of a function f is given. Use the graph to answer the question.
(-20,12) , (-12,0) , (0,-12) , (8,-16) , (12, -8), (16,8) and (20,0)

- anonymous

For what numbers x is f(x)<0 ?

- jim_thompson5910

look at the points where the y coord is negative

- jim_thompson5910

|dw:1433983055819:dw|

- anonymous

Okay and they cant be greater than 0 correct?

- jim_thompson5910

yeah because you said f(x) < 0

- anonymous

Right so how would I say this?

- jim_thompson5910

they just want you to list points?

- anonymous

OKay so in this case it would be (-12,0)

- jim_thompson5910

if that's the case, then list any points with y coordinates less than 0

- anonymous

It asks me For what numbers x is f(x)<0

- jim_thompson5910

what are the x intercepts of that graph

- anonymous

-20 , -16, -12, -8, -4,0 4, 8, 12, 16 and 20

- jim_thompson5910

|dw:1433983321114:dw|

- anonymous

on the far left its -12 and on the far right its probably 14 because its in between 12 and 16

- jim_thompson5910

|dw:1433983408801:dw|

- anonymous

yes

- jim_thompson5910

|dw:1433983425459:dw|

- jim_thompson5910

|dw:1433983449734:dw|

- anonymous

ok

- anonymous

@jim_thompson5910

- anonymous

???

- anonymous

@jim_thompson5910 how would I write this?

- anonymous

@jim_thompson5910

- jim_thompson5910

I think they just want the x values that correspond to when y is negative

- anonymous

So would I write something like [-12, -1]

- jim_thompson5910

where are you getting -1?

- anonymous

idk? I am guessing that this is correct? but I have no clue

- anonymous

[-12, 14]

- jim_thompson5910

the x intercepts are -12 and 14
the interval (-12,14) represents the region when f(x) < 0

- anonymous

OKay thank you! but wouldnt it have to be [ instead of ( ?

- jim_thompson5910

() because you don't include the points on the x axis

- jim_thompson5910

not [ ]

- anonymous

OKay I got cha awesome thank you so so so much your amazing :D

- jim_thompson5910

yw

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