Evaluating a Function
You evaluate a function by "plugging in a number".
For example, to evaluate the function
f(x) = 3x2+ x -5
at x = 10, you plug in a 10 everywhere you see an x:
f(10) = 3(10)2 + 10 - 5
=3(100) + 10 - 5
=300 + 10 - 5
=305
To evaluate f at x = z + 1, you would write
f(z + 1)= 3(z + 1) 2 + (z + 1) - 5
The thing to be careful of is parentheses. Notice how in the first term, the entire expression (z + 1) is squared? If you wrote
f(z + 1) = 3z + 1 + (z + 1) - 5 (wrong!)
it would be wrong. You need the whole expression squared and multiplied by 3, and the parentheses are needed to make it happen!