anonymous
  • anonymous
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
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
@jim_thompson5910
jim_thompson5910
  • jim_thompson5910
f(x) = 5x + 1 f(1) = 5(1) + 1 ... replace every x with 1 f(1) = ???
anonymous
  • anonymous
5

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jim_thompson5910
  • jim_thompson5910
close but no
anonymous
  • anonymous
6 lol
jim_thompson5910
  • jim_thompson5910
"5(1) + 1" means "5 times 1 plus 1"
jim_thompson5910
  • jim_thompson5910
yeah f(1) = 6
jim_thompson5910
  • 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
  • anonymous
0
jim_thompson5910
  • jim_thompson5910
yep x = 0 leads to f(x) = 3
jim_thompson5910
  • jim_thompson5910
solve 3y − 7 = y + 5 for y. Tell me what you get
anonymous
  • anonymous
6
jim_thompson5910
  • jim_thompson5910
y = 6 is correct
jim_thompson5910
  • jim_thompson5910
from part a) we got f(1) = 6
anonymous
  • anonymous
ok so 1 and 3 :)
jim_thompson5910
  • jim_thompson5910
yeah
anonymous
  • anonymous
I have one last one and I'm done for tonight!
jim_thompson5910
  • jim_thompson5910
show me what you have so far
anonymous
  • anonymous
Ok. so I guess a positive end behavior for f(x)+2
anonymous
  • anonymous
yes?
jim_thompson5910
  • jim_thompson5910
how do you know it's positive?
anonymous
  • anonymous
i just assumbed bc the leading co. is positive
jim_thompson5910
  • 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
  • jim_thompson5910
what we can say is that the end behavior won't change if we add 2 to f(x)
anonymous
  • anonymous
true. I agree
jim_thompson5910
  • jim_thompson5910
f(x)+2 just shifts f(x) up 2 units
jim_thompson5910
  • 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
  • jim_thompson5910
so (-1/2)*f(x) will have its end behavior flipped
anonymous
  • anonymous
I agree.
jim_thompson5910
  • jim_thompson5910
what can you say about the y-intercept?
anonymous
  • anonymous
It would be (0,2)
jim_thompson5910
  • jim_thompson5910
but do we know what the y-intercept of f(x) is?
anonymous
  • anonymous
and increasing?
anonymous
  • anonymous
2
jim_thompson5910
  • jim_thompson5910
we don't know what the y-intercept of f(x) is
jim_thompson5910
  • jim_thompson5910
but whatever it is, it is shifted up 2 units for f(x)+2
anonymous
  • anonymous
yes. And what about the -1/2 one?
anonymous
  • anonymous
so a wide parabola?
jim_thompson5910
  • jim_thompson5910
it gets wider when you compress it vertically, yes
anonymous
  • anonymous
But I don't understand how it is increasing and the regions where it does part>>
anonymous
  • anonymous
any ideas?
jim_thompson5910
  • 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
  • jim_thompson5910
with (-1/2)*f(x), the intervals swap. Whatever was decreasing is now increasing and vice versa.
anonymous
  • anonymous
Oh:O !! That makes sooo much more sense! Thanks:)
anonymous
  • anonymous
is that it? We are done with the question
jim_thompson5910
  • jim_thompson5910
yeah I think so

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