What of the following statements have the same result?
f(1) when f(x) = 5x + 1
f−1(3) when f(x) = 2x+3
3y − 7 = y + 5

- anonymous

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- anonymous

@jim_thompson5910

- jim_thompson5910

f(x) = 5x + 1
f(1) = 5(1) + 1 ... replace every x with 1
f(1) = ???

- anonymous

5

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## More answers

- jim_thompson5910

close but no

- anonymous

6 lol

- jim_thompson5910

"5(1) + 1" means "5 times 1 plus 1"

- jim_thompson5910

yeah f(1) = 6

- jim_thompson5910

"f−1(3) when f(x) = 2x+3"
is a fancy way of saying "plug in f(x) = 3 and solve for x"
f(x) = 2x+3
3 = 2x+3
3-3 = 2x+3-3 ... Subtract 3 from both sides.
0 = 2x
x = ???

- anonymous

0

- jim_thompson5910

yep x = 0 leads to f(x) = 3

- jim_thompson5910

solve 3y − 7 = y + 5 for y. Tell me what you get

- anonymous

6

- jim_thompson5910

y = 6 is correct

- jim_thompson5910

from part a) we got f(1) = 6

- anonymous

ok so 1 and 3 :)

- jim_thompson5910

yeah

- anonymous

I have one last one and I'm done for tonight!

- jim_thompson5910

show me what you have so far

- anonymous

Ok. so I guess a positive end behavior for f(x)+2

- anonymous

yes?

- jim_thompson5910

how do you know it's positive?

- anonymous

i just assumbed bc the leading co. is positive

- jim_thompson5910

we don't know anything about the original function f(x). So we can't say if it has positive or negative end behavior

- jim_thompson5910

what we can say is that the end behavior won't change if we add 2 to f(x)

- anonymous

true. I agree

- jim_thompson5910

f(x)+2 just shifts f(x) up 2 units

- jim_thompson5910

on the other hand (-1/2)*f(x) flips f(x) over the x axis and compresses it vertically by a factor of 2

- jim_thompson5910

so (-1/2)*f(x) will have its end behavior flipped

- anonymous

I agree.

- jim_thompson5910

what can you say about the y-intercept?

- anonymous

It would be (0,2)

- jim_thompson5910

but do we know what the y-intercept of f(x) is?

- anonymous

and increasing?

- anonymous

2

- jim_thompson5910

we don't know what the y-intercept of f(x) is

- jim_thompson5910

but whatever it is, it is shifted up 2 units for f(x)+2

- anonymous

yes. And what about the -1/2 one?

- anonymous

so a wide parabola?

- jim_thompson5910

it gets wider when you compress it vertically, yes

- anonymous

But I don't understand how it is increasing and the regions where it does part>>

- anonymous

any ideas?

- jim_thompson5910

f(x) isn't given, so we cannot find the increasing/decreasing intervals. Whatever they are, they don't change when going to f(x)+2. Everything shifts up which is why the intervals don't change

- jim_thompson5910

with (-1/2)*f(x), the intervals swap. Whatever was decreasing is now increasing and vice versa.

- anonymous

Oh:O !! That makes sooo much more sense! Thanks:)

- anonymous

is that it? We are done with the question

- jim_thompson5910

yeah I think so

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