Question

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

Answer 1

@jim_thompson5910

Answer 2

f(x) = 5x + 1

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

f(1) = ???

Answer 3

5

Answer 4

close but no

Answer 5

6 lol

Answer 6

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

Answer 7

yeah f(1) = 6

Answer 8

"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 = ???

Answer 9

0

Answer 10

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

Answer 11

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

Answer 12

6

Answer 13

y = 6 is correct

Answer 14

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

Answer 15

ok so 1 and 3 :)

Answer 16

yeah

Answer 17

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

Answer 18

show me what you have so far

Answer 19

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

Answer 20

yes?

Answer 21

how do you know it's positive?

Answer 22

i just assumbed bc the leading co. is positive

Answer 23

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

Answer 24

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

Answer 25

true. I agree

Answer 26

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

Answer 27

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

Answer 28

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

Answer 29

I agree.

Answer 30

what can you say about the y-intercept?

Answer 31

It would be (0,2)

Answer 32

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

Answer 33

and increasing?

Answer 34

2

Answer 35

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

Answer 36

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

Answer 37

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

Answer 38

so a wide parabola?

Answer 39

it gets wider when you compress it vertically, yes

Answer 40

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

Answer 41

any ideas?

Answer 42

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

Answer 43

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

Answer 44

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

Answer 45

is that it? We are done with the question

Answer 46

yeah I think so