Question

y=9-3^x
what is the domain, range and intercepts of this function?

Answer 1

1) domain is all real numbers because you can raise 3 to any power
2) range is \[(-\infty, 9)\] since
\[3^x>0\] and so
\[-3^x< 0\] for all x, therefore
\[9-3^x<9\] always

Answer 2

y intercept is what you get when x = 0, so it is
\[9-3^0=9-1=8\] or as a coordinate (0,8)

Answer 3

and finally x intercept is what you get if you put y = 0 solve
\[9-3^x=0\]
\[9=3^x\]
\[x=2\] so it is (2,0)

Answer 4

Thank you