Question

HELP ME PLEASE
Which of the following exponential functions goes through the points (1, 6) and (2, 12)?

f(x) = 3(2)x
f(x) = 2(3)x
f(x) = 3(2)−x
f(x) = 2(3)−x

Answer 1

Plug in x=1 and see if it equals 6
Plug in x=2 and see if it equals 12

Make sense?

Answer 2

not really? can you guide me through it? (xD I dont want to be an answer-hogger/wanter.. I dont want the answer, just explanations :) ) @freckles

Answer 3

Do you understand that coordinates are in the form (x,y)?

Answer 4

yes. @BMF96

Answer 5

f(x) = y

Answer 6

What don't you understand?

Answer 7

If \[\Large f(x) = 7(3)^x\] (for example), then what is the value of f(x) when x = 2? In other words, what is f(2) equal to?

Answer 8

f(2)=441?? #CONFUSED

Answer 9

Replace each x with 2
\[\Large f(x) = 7(3)^x\]
\[\Large f(2) = 7(3)^2\]
\[\Large f(2) = 7(9)\]
\[\Large f(2) = 63\]
Do you see how I got f(2) to be equal to 63?

Answer 10

btw you square first and then you multiply

Answer 11

ok, I forgot that rule :) (like DUHR, Bella, get a grip)

Answer 12

Since \(\Large f({\color{red}{2}}) = {\color{blue}{63}}\) from my example, this means the point \(\Large ({\color{red}{x}},{\color{blue}{y}})=({\color{red}{2}},{\color{blue}{63}})\) lies on the function curve of f(x)

Answer 13

okayyy....

Answer 14

\(f(x)=y=
\begin{cases}
3(2)^x\\
2(3)^x\\
3(2)^{-x}\\
2(3)^{-x}
\end{cases}\qquad \qquad
\begin{array}{llll}
x&y
\\\hline\\
{\color{brown}{ 1}}&3(2)^{\color{brown}{ 1}}\\
&2(3)^{\color{brown}{ 1}}\\
&3(2)^{-{\color{brown}{ 1}}}\\
&2(3)^{-{\color{brown}{ 1}}}\\
{\color{brown}{ 2}}&3(2)^{\color{brown}{ 2}}\\
&2(3)^{\color{brown}{ 2}}\\
&3(2)^{-{\color{brown}{ 2}}}\\
&2(3)^{-{\color{brown}{ 2}}}
\end{array}\)

Answer 15

so what ybarrap said at the top, you plug in each x coordinate into each function and see if you get the correct corresponding y coordinates

Let's say we pick choice B at random

\[\Large f(x) = 2(3)^x\]

The first point is (1,6). To test if this point lies on the function f(x) curve, we plug in x = 1 and see if y = 6 pops out

\[\Large f(x) = 2(3)^x\]
\[\Large f(1) = 2(3)^1\]
\[\Large f(1) = 2(3)\]
\[\Large f(1) = 6\]

It does, so (1,6) is definitely on this curve. How about (2,12)? Let's check

\[\Large f(x) = 2(3)^x\]
\[\Large f(2) = 2(3)^2\]
\[\Large f(2) = 2(9)\]
\[\Large f(2) = 18\]

Nope. The point (2,18) actually lies on this function curve and NOT (2,12). So we can rule out choice B.

Answer 16

So what just happened was that I've proven that the function \(\Large f(x) = 2(3)^x\) does NOT go through both points (1,6) and (2,12).

Answer 17

okay, so its A, C, or D lol.... so lets try to rule out A...

Answer 18

@jim_thompson5910

Answer 19

what did you get so far in checking choice A?

Answer 20

that A is, in fact NOT the answer!?

Answer 21

if x = 1, then what is f(1) ?

Answer 22

f

Answer 23

Wait, so it IS A!!!!!

Answer 24

\[\Large f(x) = 3(2)^x\]
\[\Large f(1) = 3(2)^1\]
\[\Large f(1) = \underline{ \ \ \ \ \ \ \ } \text{ (fill in the blank)}\]

Answer 25

6

Answer 26

and how about f(2)

Answer 27

12

Answer 28

Good. Choice A is definitely the answer. As practice, why not go through C and D and eliminate them.

With choice C, if x = 1, then what is f(x) equal to?