Evaluating functions

1. Evaluating Functions:
To evaluate a function, substitute the input (the given number or expression) for the function's variable (place holder, x).
Replace the x with the number or expression.
1. Given the function f (x) = 3x - 5, find f (4).
Solution: Substitute 4 into the function in place of x. f (4) = 3(4) - 5 = 7.
This answer can be thought of as the ordered pair (4,7).
The answer may also be referred to as the image of 4 under f (x).
2. Find the value of h (b) = 3b2
- 2b + 1 when b = -3.
Solution: Substitute -3 into the function in place of b. h (-3) = 3(-3)2
- 2(-3) + 1 = 34.
3. Find g (2w) when g (x) = x2
- 2x + 1.
Solution: When substituting expressions, like 2w, into a function, using parentheses will
help prevent algebraic errors. For this problem, use (2w).
g (2w) = (2w)2
- 2(2w) + 1 = 4w2
- 4w +1 (Note: the answer is in terms of w.)
4. Given f (x) = 2x2
+ 4x - 3, find f (2a + 3).
Solution: Be sure to use parentheses!
Be careful - more algebra work is needed here.
f (2a + 3) = 2(2a + 3)2
+ 4(2a + 3) - 3
= 2(4a2
+ 12a + 9) + 8a + 12 - 3
= 8a2
+ 24a + 18 + 8a + 12 - 3
= 8a2
+ 32a + 27
Did you multiply?
5. Given f (x) = x2
- x - 4. If f (k) = 8, what is the value of k?
Solution: Set the function rule equal to 8 and solve for k.
x2
- x - 4 = 8
x2
- x - 12 = 0
(x - 4)(x + 3) = 0
x - 4 = 0; x + 3 = 0
x = 4; x = -3
The value of k can be either 4 or -3.
To review on how to evaluate a function please click or copy the video link below to watch a video
on how to evaluate a function.
 https://www.youtube.com/watch?v=PBimjTtsJQY (Evaluating a Function)