 Evaluating Functions MathBitsNotebook.com Terms of Use   Contact Person: Donna Roberts  You worked with "evaluating functions" in Algebra 1. To evaluate a function, substitute the input (the given number or expression) for the function's variable (place holder, such as x). Just replace the x with the number or expression, using parentheses where needed. Let's take a look at situations that require a bit more sophistication.
1.
Given the function f (x) = 5x + 4, find f (2m).

Solution:
Substitute 2m into the function in place of x.        f (2m) = 5(2m) + 4 = 10m + 4.
Using parentheses will avoid problems.
Notice that the answer is an algebraic expression, not a numeric value.
2.
Given f (x) = 3x2 + 2x - 3, find f (2a - 5).

Solution:
Parentheses are a MUST is this problem!
Be careful - more algebra work is needed here.

f (2a - 5) = 3(2a - 5)2 + 2(2a - 5) - 3
=
3(4a2 - 20a + 25) + 4a - 10 - 3
= 12a2 - 60a + 75 + 4a - 10 - 3
=
12a2 - 56a + 62
3.
Given g (a) = 9 - a2 and h (a) = a - 3, express:
 a) g (a) + h (a) b) g (a) - h (a) c) g (a) • h (a) d) , g(a) ≠ 0

Solution:
 a) g (a) + h (a) = (9 - a2) + (a - 3) = -a2 + a + 6 b) g (a) - h (a) = (9 - a2) - (a - 3) = -a2 - a + 12 c) g (a) • h (a) = (9 - a2) • (a - 3) = -a3 + 3a2 + 9a - 27 d) a ≠ 3; a ≠ -3
4.
Given , express .

Solution: Warm up your algebraic fraction skills! 5.
Given f (x) = x2 - x - 4. Find f (x + h).

Solution: Be careful to replace the x with (x + h). Use parentheses!!!!
 (x+h)2 - (x+h) - 4 x2 + 2xh + h2 - x - h - 4
6.
Given g(x) = x2 + 1 and h(x) = 5 - x. Express 3•g(5 - x) - 2•h(x2)

Solution:
Remember to use parentheses!
3g(5 - x) - 2h(x2) = 3((5 - x)2 + 1) - 2(5 - x2) = 3(x2 - 10x + 25 + 1) - 2(5 - x2)
= 3x2 - 30x + 78 - 10 + 2x2 = 5x2 - 30x + 68
7. Solution: FYI: This new expression is called the "difference quotient" or average rate of change.    For calculator help with evaluating expressions and functions click here. NOTE: The re-posting of materials (in part or whole) from this site to the Internet is copyright violation and is not considered "fair use" for educators. Please read the "Terms of Use".