Y=ln(x+2) need help have a quiz soon?

Question

i have to graph it
need to find the domain
also the range.

The problem is i dont know where to start if someone could give me a step by step way to answer this problem i will be at ya 10 point mercy

Answer 1

Graphing it: Why not do it the old fashioned way?
set x=0 and see what you get for y. Plot the point.
set x=1 and see what you get for y. Plot the point.
set x=-1 and see what you get for y. Plot the point.
Try a few other values. Plot the points. There's really not much of shortcut to this.

The domain. That means, what values of x will "work"? Are there any values of x, positive, negative or zero, which you CANNOT plug into ln(x+2) ? [Hint: Northstar is wrong: the domain is NOT x>0. ]

The range. That means, what are the values of Y that will come out? If you try "extreme" values of x, what are the smallest/largest values of Y that will come out?

Answer 2

You can only take a log of a positive number. Logs of negative numbers or zero are undefined.

So the domain is x > 0.

The log of a number
x > 1 → log is positive
x = 0 → log is zero
0 < x < x → log is negative

So the range is all real numbers.

Answer 3

ln is natural log,
1. put in an x value
2. add two to the value
3. take natural log of the the two added values, ( natural logs should be on your calculator )
4. that is your Y value

plot x,y values

take x from like 1 to 10 or so

be carefull with low values, don't use negative negative numbers

Answer 4

y = ln(x+2)
The domain is (-2, + infinity)
The range is (-infinity, + infinity)
The curve starts in the 3rd quadrant with x>-2 and y a large negative number. It crosses the x axis at (-1,0), crosses the y-axis at (0,ln(2)) and then slowly rises to infinity as x--> infinity