SOLUTION: Find the domain and range of the function f(x)=-e^-x+8

Question 1145473: Find the domain and range of the function f(x)=-e^-x+8
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
let f(x) = y
you get y = -e^-x + 8
this is equivalent to:
y = -1/e^x + 8
as x gets larger, -1/e^x becomes smaller and approaches 0.
that makes y approach 8.
as x gets smaller, e^x gets smaller which makes -1/e^x become larger until it approaches minus infinity.
there is no restriction to the value that x can take, therefore the domain is -infinity < x < infinity.
the range becomes -infinity < y < 8.
that's what i think.
the graph looks like this.

$$$

you can test additional values by simply replacing x with random numbers such as 10, 50, 100, 0, -10, -50, -100
you'll get values up to the ability of the calculator to handle the largeness or the smallness of the value of y.
for example:
y = -1/e^50 + 8 yields y = 8
y = -1/e^-50 + 8 yields y = -5.18..... * 10^21
y = -1/e^500 + 8 yields overflow
y = -1/e^-500 + 8 yields divide by 0 error.
the calculator could handle e ^ plus or minus 50, but it couldn't handle e ^ plus or minus 500 since the resulting number was greater than the maximum value the calculator could handle.

RELATED QUESTIONS
please help me find the domain range and asymtope of this function f(x)=... (answered by user_dude2008)

Find the domain and the range of the function:... (answered by edjones)

find the domain and range of the following function f(x) =... (answered by Theo)

Find the domain and range of the function... (answered by lwsshak3)

State the domain and the range of the exponential function... (answered by stanbon,solver91311)

Consider the function f defined by f(x) = 8^x how do i find the domain and range of... (answered by stanbon)

f(x)=2+e^x a)find the inverse function f^-1(x) b)fine the domain and range of... (answered by stanbon)

f(x)-2+e^x a)find the inverse function f^-1(x) b)fine the domain and range of... (answered by stanbon)

what is the domain and range of the function.... f(x)= 4/x +... (answered by lwsshak3)