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!