What is the answer for question 8) ?

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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.

**Sources:**

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