Find the asymptote of y = 3^(x + 1) + 1

[Wezmur]

hi,

could anyone here help me how to find the asymptote of y = 3[sup:1vt9dlkh]x+1[/sup:1vt9dlkh] + 1

I already solve for y but I'm still trying to understand how asymptote work to be able to graph the function.

thanks in advance.

 

[Deleted member 4993]

Re: pre-calc question

hi,

could anyone here help me how to find the asymptote of y = 3[sup:3n5df7rg]x+1[/sup:3n5df7rg] + 1

I already solve for y but I'm still trying to understand how asymptote work to be able to graph the function.

thanks in advance.

Get a graphing calculator and look at the graph of the function.

See where the assymptote is.

Then try to justify - why it should be so.

Try to see - as 'x' becomes a very large 'negative' number - what happens to 'y'.

If you still cannot understand - come back and tell us what you found - we'll go from there.

 

[soroban]

Re: pre-calc question

Hello, Wezmur!

Could anyone help me find the asymptote of: .\(\displaystyle y \:= \:3^{x+1}+ 1\)

\(\displaystyle \text{We are expected to know the graph of: }\;y \;=\;a^x\quad\text{ for }a > 0,\:a \neq 1\)

                      |
                      |       *
                      |
                      |     *
                      |    *
                      |  *
                     1*
                  *   |
            *         |
    *                 |
  --------------------+----------
                      |

It has y-intercept (0,1), soars upward to the right
. . and approaches the x-axis as an aymptote to the left.
Hence, this is the graph of: .\(\displaystyle y \;=\;3^x\)



The graph of: .\(\displaystyle y \:=\:3^{x+1}\) is the same graph moved one unit to the left.

                         |    *
                         |
                         |  *
                         | *
                        3*
                      *  |
                  *      |
            *            |
    *                    |
  -----------------------+----------
                         |

The graph of \(\displaystyle y \:=\:3^{x+1}+1\) is the previous graph moved up one unit.

                         |    *
                         |
                         |  *
                         | *
                        4*
                      *  |
                  *      |
            *            |
    *                    |
  - - - - - - - - - - - -+ - - - - -
                         |
  -----------------------+----------
                         |

And we see that the horizontal asymptote is: .\(\displaystyle y \:=\:1.\)

 

[Wezmur]

Re: pre-calc question

hey soroban, thanks for the reply. So basically what you are saying is that I should be able to draw a graph just by looking at the equation even without a graphing calculator?

 

[jonboy]

Re: pre-calc question

yes you should be able to. but eventually you should be able to mentally do the process soroban done.

 

[Wezmur]

Re: pre-calc question

ok, thanks. Now I know what I need to study more.

p.s.
thanks also to Subhotosh Khan. Your answer to my question helps me understand the concept too.