Hi,

y= Note: Domain of  is the same as the domain of =

 x-intercept is when y = 0, it is (-16,0)  3^0 = 1 = x+17, 

 y-intercept is when x = 0

   y =  = log 17^4/log 3  || log  base ten 

Answer by Edwin McCravy(20056)   (Show Source): You can put this solution on YOUR website!
 
If you have a graphing calculator, I would suggest always drawing the 
graph first.  Here is the graph:

 

The graph has a vertical asymptote x = -17 (the green line).

Logarithms are only taken of positive numbers.  To get that domain,

set x + 17 > 0
         x > -17

The domain is {x|x > -17} 

In interval notation that's written (-17,)

To find the y-intercept:

Set x = 0,

y =  

y= =  = 10.31560769

So the y-intercept is (0, 10.31560769)

To find the x-intercept,

Set y = 0

y =  = 0

 = 0

Divide both sides by 4

 = 0         

Write the equivalent exponential form of that equation:

x + 17 = 30
x + 17 = 1
     x = -16

So the x-intercept is (-16,0).  As you see all these check with the graph. 

Edwin
 

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