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What is the answer for question 8) ? http://postimg.org/image/5gm0wsol3/

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lkballer24 | Student, Grade 11 | Valedictorian

Posted May 23, 2013 at 10:26 PM via web

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What is the answer for question 8) ?

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crmhaske | College Teacher | (Level 3) Associate Educator

Posted May 23, 2013 at 10:52 PM (Answer #1)

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An asymptote is a line for which the function approaches infinity or becomes undefined as the distance between the function and the line approaches 0.

For the function y=log(x+3), y is undefined at x=-3 because the log of any number less than or equal to zero does not exist.

Therefore there is a vertical asymptote at x=-3

In order to determine if there is a horizontal asymptote, we must rearrange the equation to be a function for x:

`10^y=x+3`

`x=10^y-3`

There is no horizontal asymptote because as y approaches infinity so does x.

The x-intercept exists when y=0:

0=log(x+3)

10^0=x+3=1 ->x=-2

Therefore the x-intercept is at (-2,0)

The y-intercept exists when x=0:

y=log(0+3)=0.48

Therefore the y-intercept is at (0,0.48)

The domain of a function is the range of all possible x values.  The domain of y=log(x+3) is x>-3

The range of a function is the range of all possibly y values.  The range of y=log(x+3) is `-ooltyltoo` because the integer 10 can be raised to all real exponents.

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