Graph an exponential function f(x) whose domain is all real numbers and is such that: f(x) is decreasing over it's entire domain, f(x)=3 as x approaches - infinity, f(x)=-infinity as x approaches +infinity. Its a little confusing on these limits, thanks.

Question

anonymous · Answer

The range of the exponent function, $$f(x)=e^x$$ is $$(0,\infty)$$ .
The range of $$f(x)=-e^{x}$$ is $$(0,-\infty)$$ if you add a constant, k, the function becomes $$f(x)=-e^x+k$$ with a range of 
$$(k,-\infty)$$
k=3, $$f(x)=-e^x+3$$

tkhunny · Answer

If you build it, you will see it.

f(x) = e^x  Domain is good, but -infty ==> 0 and +infty ==> +infty

We're upside down.

f(x) = -e^x  Domain is good and +infty ==> -infty, but -infty ==> 0

We're three low.

f(x) = 3-e^x  Domain is good, -infty ==> 3 and +infty ==> -infty

Done.

anonymous · Answer

|dw:1350800041885:dw|