SOLUTION: Evaluate the exponential function for three positive values of x, three negative values of x, and at x=0. Show your work. Use the resulting ordered pairs to plot the graph; submit
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Question 285765: Evaluate the exponential function for three positive values of x, three negative values of x, and at x=0. Show your work. Use the resulting ordered pairs to plot the graph; submit the graph via the Dropbox. State the domain and the range of the function.
f(x) = e^x + 5
Please use the following values for x so I can check my work against yours:
1
2
3
0
-1
-2
-3
Please also give the domain and range of the function.
Thanks a ton! Answer by jsmallt9(3758) (Show Source):
*** Additional note: "e" is a special number like . If your calculator does not have a button for "e" then use 2.7182818284590451 (or a rounded-off version of this number) for "e". Then raise this number to "x" power and then add 5. On many calculators you can just type:
2.718^3+5
followed by the "=" or "Enter" key and it will calculate f(3) for you. Then just keep changing the "3" to the other values of "x" you are supposed to use. (If your calculator does not have a "^" key, then use a key that looks like: )***
The domain is the set of possible values for x. x is an exponent in your function and exponents can be any number. So the domain is all real numbers.
The range is the set of possible values for y or f(x). Since f(x) is the sum of and 5, we need to know what values can have. e is a positive number and a positive number, raised to any power must be a positive number. It cannot be zero and it cannot be negative. (Remember and a negative exponent means a reciprocal (and a reciprocal of any power of e is still positive)).
can be any positive number -- from just barely above zero (when x is a large negative number) to extremely large positive numbers. And since , f(x) can be any number greater than 5.
(