functionfactory4
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) funcdiv, 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) hans2
a ≠
3; a ≠ -3
4.
Given mx, express mx2.

Solution: Warm up your algebraic fraction skills!
in
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.
dq1
Solution: FYI: This new expression is called the "difference quotient" or average rate of change.

dq2a

dq3a

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For calculator help with
evaluating expressions and functions
click here.


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