Question

so if I have Y=e^(x-1)-1 find the range

Answer 1

\[e^x>0\] so
\[e^{x-1}-1>-1\]

Answer 2

can the domain be -infinity to infinity

Answer 3

From -0.4 to infinity according to the graph

Answer 4

yes, you can raise e to any power

Answer 5

can I put that in the calculsator and come up with the answer?

Answer 6

You can come up to the answer using graphing calculator.

Answer 7

I have that kind

Answer 8

When you will see the graph then you can see the graph is going upwards from -0.4 towards infinity so range will be infinity.

Answer 9

so the domain and range is the same
Im confused

Answer 10

For domain part you have to check all possible values of x, and when you will see the graph then you can see the graph is going from extreme left side towards extreme right side so domain will be from -infinity to +infinity.

Answer 11

Always see horizontal line for domain part and vertical line for range part, because domain is all possible values of x and range is all possible values of y.

Answer 12

ok so I had them back words that would make more sense to me now

Answer 13

Yes!

Answer 14

Do you have any doubt do far?

Answer 15

*so

Answer 16

no it makes more sense now

Answer 17

Great!:)

Answer 18

Thanks

Answer 19

now if I have to find the y intercept of this same equation do I do it as follows

Answer 20

For finding y-intercept we just plug 0 in place of x, or according to the graph just see, at which point graph is cutting the y-axis. because at y-axis the value of x is always equal to 0.

Answer 21

So you can see at the point y=-0.4 the graph is cutting the y-axis, so y=-0.4 will be the answer for y-intercept.

Answer 22

Is this clear so far Danyel?

Answer 23

\[ y=e ^{(0-1)}-1\]

Answer 24

ok yes it makes sense

Answer 25

Okay! so it is equal to y=e^(-1)-1, or y=1/e-1.and value of 1/e is 0.3678

Answer 26

So .3678-1 is equal to -0.63, but you will see the graph then you will see the exact value.

Answer 27

And -0.63 and -0.4 are vary closer number, so if it is saying in the problem to find the answer using graph then we can say y-intercept as -0.4 and if use of graph is not allowed then answer will be -0.63

Answer 28

Does this make sense to you?

Answer 29

it says to graph the function then find all these and the asymptote as well

Answer 30

so yes I use the graph right

Answer 31

Okay! so we can use graphing calculator, because it is too lengthy to plot the graph of given exponential function, so our answer for y-intercept will be y=-0.4

Answer 32

Yes! you are correct!

Answer 33

yes this makes much better sense thank you

Answer 34

You are most welcome!:)

Answer 35

You have to find asymptote or you will do it by your own?

Answer 36

I have to find it but I think it might be -1

Answer 37

Can you recheck it again? It will be equal to 1

Answer 38

By the way we have three rules also for finding horizontal asymptote.

Answer 39

If the degree (the largest exponent) of the denominator is bigger than the degree of the numerator, the horizontal asymptote is the x-axis (y = 0).

Answer 40

If the degree of the numerator is bigger than the denominator, there is no horizontal asymptote.

Answer 41

what are those I haven't heard them

Answer 42

If the degrees of the numerator and denominator are the same, the horizontal asymptote equals the leading coefficient (the coefficient of the largest exponent) of the numerator divided by the leading coefficient of the denominator).

Answer 43

These are three rules for finding horizontal asymptote and for vertical asymptote we simply equate denominator with 0.

Answer 44

Did you get these points?

Answer 45

yes

Answer 46

so does that mean we have o asympyote then herewith this one

Answer 47

These all rule will not apply for this problem, these rules will apply when we have given fractional equation. we will get the horizontal asymptote from the graph in this problem.

Answer 48

ok that is what I thought but had to check.
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Answer 49

so when I look at the graph It looks like -1

Answer 50

For horizontal asymptote we will see at which point the graph is cutting the horizontal line, Isn't it going through the point x=1 at the x-axis?

Answer 51

yes i was thinking the y axis

Answer 52

Not really! Here answer will be 1.

Answer 53

Do you have any question so far?

Answer 54

no

Answer 55

thank you sooooo much

Answer 56

You are most welcome!:) Have a nice time ahead! Take care! Bye!

Answer 57

bye