for function f (x) =x2-5x find each of the following a. f(-2), b. f(1), c. f(-1), d.f(2), e. f(10)

Question

I would like to see the steps I am lost on this one

Answer 1

f(x) = x² - 5x

 

Ralph, a functions is like a manufacturing machine.  You put something into it, and you get something, only one thing, out of it.

 

The function definition tells you exactly what to do with what you put in.  In this case the definition is f(x) = x² - 5x. To calculate the output of the function, you just take the specific value you're taking the function of -- the number inside the parentheses -- and substitute it for the variable in the definition.

 

Let's try one.  Let's try (b) because f(1) is usually very easy to calculate.

 

So...

 

f(x) = x² - 5x

 

To find f(1), just substitute 1 for x and do the calculations.

 

f(1) = 1² - 5*1 = 1 - 5 = -4

 

Try another:

 

f(-2) = (-2)² - 5(-2) = 4 - (-10) = 4 + 10 = 14

 

And the rest:

 

f(-1) = (-1)² - 5(-1) = 1 - (-5) = 1 + 5 = 6

 

f(2) = 2² - 5(2) = 4 - 10 = -6

 

f(10) = 10² - 5(10) = 100 - 50 = 50

 

 

Answer 2

A function has a single value for each allowable value appropriate to the range of the function.
 
So, f(x) has one value for x=-2, we call that f(-3), and one value for x=1, we call that f(1).
 
Since we are finding f(x) values for x=-2 and for x=1 and ... , we just replace x with those values in the formula (function expression).

 

f(-2) = (-2)^2 -5*(-2)     simple math from here

f(1)  =  (1)^2 - 5*(1)      actually, typing this is harder than solving the problem.

 

Be sure to do parts c, d, e, and f.    (always re-read the question to be sure you answered everything)