"Give the range of the function."?

Question

f(x) = 2x + 3.

Give the range.
Should turn out to be : 3 (less than or equal to) f(x) (less than or equal to) 23.

I don't have ANY clue on how to get it, with or without a calculator. Without the calculator type, would be easiest for me to understand.
Please, don't be shy with the details.
Ever since Algebra I, I B.S.'d everything. Now it's all caught up with me in Trig./Pre.Calc.

Answer 1

We need to know a little about the domain (the values of x), which you seem to have left out.

From what you have described, the values of x are given as 0 <= x <= 10. I'll just assume this is what you left out.

Since this is a straight line, the function f(x) will have a range (values for f(x)) that goes from f(0) to f(10). So, plug in the lower and upper values of x to get f(x)
f(0) <= f(x) <= f(10)

f(0) = 2(0) + 3 = 3
f(10) = 2(10) + 3 = 23

So the range is:
3 <= f(x) <= 23

* P.S. Congratulations on the Bachelor of Science in everything else... that is what B.S. stands for, right?

Answer 2

First we have to get the domain of the function which is
from (-infinite to +infinite)
So we take the values that we think are the easiest:
-3, -2, -1, 0, 1, 2, 3
and we sustite them on the function to get f(x) which is the range
2(-3) +3 = -3
2(-2) +3 = -1
2(-1) +3 = 1
2(0) +3 = 3
2(1) +3 = 5
2(2) +3 = 7
2(3) +3 = 9

we could go on and on and the range would go on and on as well. So the range of your function is from (-infinite to +infinite)