SOLUTION: I think my graph is right, but I did it by substitution.. I can't get the X-intercept to match my graph... Graph the function f(x)= 2 * (3^x) - 5. Indicate the horizontal asym

Algebra ->  Graphs -> SOLUTION: I think my graph is right, but I did it by substitution.. I can't get the X-intercept to match my graph... Graph the function f(x)= 2 * (3^x) - 5. Indicate the horizontal asym      Log On


   

Question 34527: I think my graph is right, but I did it by substitution.. I can't get the X-intercept to match my graph...
Graph the function f(x)= 2 * (3^x) - 5. Indicate the horizontal asymptote (which I believe is y=-5) also find the X-intercept (exact solution and then round to four decimal places.)
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
I'll try to plot some points and then refer to the graph
y-intercept:
y+=+2+%2A+3%5E0+-+5
3%5E0+=+1
y+=+2+-+5
y+=+-3
when x = 0, y = -3
-----------------------
x-intercept:
0+=+2+%2A+3%5Ex+-+5
2+%2A+3%5Ex+=+5
3%5Ex+=+5%2F2
take log base 10 of both sides
log%283%5Ex%29+=+log%285%2F2%29
x+%2A+log%283%29+=+log%285%29+-+log%282%29
+x+=+%28log%285%29+-+log%282%29%29+%2F+log%283%29
+x+=+%28.699+-+.301%29+%2F+.477
x+=+.834
when y = 0, x = .834
-----------------
asymptote:
When x approaches -infinity, 2 * 3^x approaches 0,
and y approaches -5
+graph%28+400%2C+400%2C+-5%2C+3%2C+-6%2C+4%2C+2%2A%283%5Ex%29-5%29+