Question

For the graphed function f(x) = −(5)x − 3 + 2, calculate the average rate of change from x = 4 to x = 6.

Answer 1

what is \(f(4)\)?

Answer 2

I have no idea! I am so confused with this

Answer 3

oooh i see, it is
\[f(x)=-5^{x-2}+3\]??

Answer 4

the options are:
-68
-60
68
60

Answer 5

yeahh it is

Answer 6

i meant
\[f(x)=-5^{x-3}+2\]

Answer 7

yes the last one is correct!

Answer 8

ok first of the average rate of change is negative, because the function is decreasing (going down)
is that clear?

Answer 9

yes

Answer 10

we need
\[f(6)=f(x)=-5^{6-2}+3\]

Answer 11

oops i just meant
\[f(6)=-5^{6-2}+3\] so lets compute it

Answer 12

it is 628

Answer 13

right?

Answer 14

\[5^4=625\] so
\[-5^4+3=-622\] if my arithmetic is correct

Answer 15

i think my answer is right, you forgot the minus sign in front i believe

Answer 16

nope i used the minus sign. if you multiply the -5 fourtimes, it is 625.

Answer 17

we also need
\[f(4)=-5^{4-2}+3=-5^2+3=-25+3=-22\]

Answer 18

oh dear hold the phone!

Answer 19

order of operations here
first exponent, then minus sign

Answer 20

so \[-5^5=-5\times 5\times5\times 5=-625\] not
\[(-5)\times (-5)\times (-5)\times (-5)=625\]

Answer 21

clear?

Answer 22

alright

Answer 23

ok now we have the numbers we need
\[f(6)=-622\]
\[f(4)=-22\] your job for the average rate of change is just like the slope of a line
\[\frac{f(6)-f(4)}{6-4}=\frac{-622-(-22)}{2}\]

Answer 24

-300

Answer 25

yes, but i see i am an idiot and used the wrong function, so we have to start again

Answer 26

alrighty lol

Answer 27

\[f(x)=-5^{x-3}+2\] is the right one

Answer 28

\[f(6)=-5^{6-3}+2=-5^3+2=-123\]

Answer 29

\[f(4)=-5^{4-3}+2=-5+2=-3\]

Answer 30

the answer is -60?

Answer 31

then \[\frac{f(6)-f(4)}{6-4}=\frac{-123-(-2)}{2}\]

Answer 32

damn typo!\[\frac{f(6)-f(4)}{6-4}=\frac{-123-(-3)}{2}\]

Answer 33

yeah i get \(-60\)

Answer 34

lol cool! thanks!!

Answer 35

via
\[\frac{-120}{2}\]

Answer 36

could you help me with another question?

Answer 37

i hope the method was more or less clear
we did it twice (once with the wrong function) but the method is the same no matter what

Answer 38

sure but i have to go soon so go ahead and post now
you can put it here if you like

Answer 39

What transformation has changed the parent function f(x) = log3x to its new appearance shown in the graph below?

Answer 40

choices are:
f(x + 4) + 2

f(x − 2) − 2

f(x + 2) + 2

f(x − 4) − 2

Answer 41

i take it it is
\[f(x)=\log_3(x)\]

Answer 42

yes

Answer 43

nevermind

Answer 44

it is 3x, together

Answer 45

\[\log(3x)\]

Answer 46

\[ \log _{3x}\]

Answer 47

lol

Answer 48

the 3 is below right?

Answer 49

yes

Answer 50

like
\[\log_3(x)\]

Answer 51

no, the 3x is together

Answer 52

ok we see a vertical asymptote at \(x=-4\) instead of at \(x=0\) so we know it has shifted to the left 4 units
that means we know it should look like
\[f(x+4)+c\] for some \(c\)

Answer 53

oo okay

Answer 54

which means we don't really care what log it is, since there is only one choice with that option

Answer 55

okay cool! thanks so much!

Answer 56

yw

Answer 57

btw it is definitely
\[f(x)=\log_3(x)\] because now we have
\[\log_3(x+4)+2\] and if \(x=-1\) the we get
\[\log_3(-1+4)+2=\log-3(3)+2=1+2=3\] which is why we see \((-1,3)\) on the graph