Question 285765
{{{f(x) = e^x + 5}}}
As far as evaluating the function, I'll leave that up to you and your calculator.<br>
*** Additional note: "e" is a special number like {{{pi}}}. 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: {{{x^y}}})***<br>
The domain is the set of possible values for x. x is an exponent in your function and exponents can be <i>any</i> number. So the domain is all real numbers.<br>
The range is the set of possible values for y or f(x). Since f(x) is the sum of {{{e^x}}} and 5, we need to know what values {{{e^x}}} can have. e is a positive number and a positive number, raised to <i>any</i> power must be a positive number. It cannot be zero and it cannot be negative. (Remember {{{e^0 = 1}}} and a negative exponent means a reciprocal (and a reciprocal of any power of e is still positive)).<br>
{{{e^x}}} 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) = e^x + 5}}}, f(x) can be any number greater than 5.<br>
Here's a graph for you to check against:
{{{graph(400, 400, -5, 5, -1, 9, e^x + 5)}}}