More Practice with Function Notation

Recall from Introduction to Function Notation that
a function is a rule that takes an input, does something to it,
and gives a unique corresponding output.

There is a special notation (called ‘function notation’) that is used to represent this situation:
if the function name is $\,f\,$, and the input name is $\,x\,$,
then the unique corresponding output is called $\,f(x)\,$.
The notation ‘ $f(x)\,$’ is read aloud as: ‘ $f\quad$ of $\quad x\,$ ’.

What exactly is $\,f(x)\,$?
Answer: It is the output from the function $\,f\,$ when the input is $\,x\,\,$.

This exercise gives more advanced practice with function notation.

EXAMPLES:

Question:
Let $\,f(x) = x^2 + 2x\,$.
Find and simplify: $f(-3)$

Solution:
$f(-3) = (-3)^2 + 2(-3) = 9 - 6 = 3$

Question:
Let $\,f(x) = x^2 + 2x\,$.
Find and simplify: $f(x+1)$

Solution:
$f(x+1) = (x+1)^2 + 2(x+1) = x^2 + 2x + 1 + 2x + 2 = x^2 + 4x + 3$

Question:
Let $\,f(x) = 5\,$.
Find and simplify: $f(x+1)$

Solution:
The function $\,f\,$ is a constant function:
no matter what the input is, the output is $\,5\,$.
That is, $\,f(\text{anything}) = 5\,$.
So, $\,f(x+1) = 5\,$.

Question:
Let $\,f(x) = x^2 - 2x\,$.
Find and simplify: $f(1) + f(3)$

Solution:

$f(1) + f(3)$

$\ \ = \overset{f(1)}{\overbrace{(1^2 - 2\cdot 1)}} + \overset{f(3)}{\overbrace{(3^2 - 2\cdot 3)}}$

$\ \ = (1 - 2) + (9- 6)$

$\ \ = 2$

Master the ideas from this section
by practicing the exercise at the bottom of this page.

When you're done practicing, move on to:
Domain and Range of a Function

(MAX is 11; there are 11 different problem types.)