Question

I have some general questions about exponential functions.

Answer 1

Type them please:)

Answer 2

Is the domain ALWAYS going to be all real numbers?

Answer 3

and I know that when you have \(y=ab^x\), the y-intercept is equal to (0,a) but what if you have, for example, \(y=4^x\), is there a way to find a, other than graphing it or making a table to find the y-intercept, thus finding a?

Answer 4

@rational

Answer 5

@quickstudent

Answer 6

@rational will you please come help? Nobody else is.

Answer 7

1*4^x ... what is a?

Answer 8

or, y=a when x=0

what is 4^0?

Answer 9

well 1, but how do I know it's 1*4 and not 2*2, is what I'm trying ask, I guess.

Answer 10

because 4^x is defined as b^x

Answer 11

1 * (2*2)^x is still 1*4^x

Answer 12

1 * (2*2)^x is not 1*2*2^x

Answer 13

Oh, okay.

Answer 14

the exponent is a grouping symbol

( )^x whatever is inside of it is grouped and you must follow the order of operations

Answer 15

That makes more sense. So, if it doesn't have something like \(y=12(0.95)^x\), is a automatically 1?

Answer 16

In that equation, a is 12... but if it's not split up, it's 1, correct?

Answer 17

yes, mathmatikers dont like writing a 1 in front of things.

1*x means that we have only one x; so 1*x = x

Answer 18

yes, a=12 in that case, if its not split then its 1

Answer 19

Okay. See, I'm learning this on my own, and I want to make sure I'm not teaching myself incorrectly XD

Answer 20

itll be fine :)

Answer 21

I have more questions :D I'm a question asker. xp

Answer 22

So, will the x-axis always be an asymptote?

Answer 23

no

Answer 24

if we move the function up or down, we move the asymptote

Answer 25

y = ab^x + k has an asymptote as y=k

Answer 26

Ohhh, I haven't gotten that far in my textbook, I guess.

Answer 27

It says that if a>0 and b>1, that the function represents an exponential growth and that if a>0 and 0<b<1 it represents an exponential decay... but what if a<0?

Answer 28

I think I may be getting ahead of myself... sorry.

Answer 29

if a is <0 youve flipped the graph upside down ...

Answer 30

ab^0 = a*1
-ab^0 = -a*1

Answer 31

if b = 1/c

(1/c)^x = c^(-x)

Answer 32

I understand what you mean by flipping the graph, but what do you mean by the last thing you put? @amistre64

Answer 33

have you worked with fraction before?

Answer 34

the x variable is the rate of change

if its negative, we are decreasing
if its positive, we are increasing

if b is a value between 0 and 1, then its essentially a fraction

applying fraction rules, we just see that we can get a -x to indicate it is decreasing is all

Answer 35

if b=1/3

(1/3)^(x) = 3^(-x)

Answer 36

ohhhhhhh. okay.

Answer 37

Thank you.

Answer 38

your welcome