In order to evaluate a function, use substitution and PEMDAS to calculate the value of the function. Many iterations of different variable values will produce multiple solutions. Eventually, these solutions can be turned into ordered pairs and the function can then be graphed. For now, we will just evaluate expressions using a single value.
Example 1:
Evaluate the function: f(x) = 4 + 3x for f(2)
Solution:
f(2) means the variable x = 2. Substitute 2 into the equation for x, then simplify using PEMDAS.
f(x) = 4 + 3x
f(2) = 4 + 3(2)
f(2) = 4 + 6
f(2) = 10
The solution 10.
Notice in the example above, the left-side of the equation doesn't change. All calculations occur on the right-hand side of the equals sign.
Example 2:
Evaluate the function: g(x) = | x + 5 | for g(-7)
Solution:
g(-7) means the variable x = -7. Substitute -7 into the equation for x, then simplify using PEMDAS.
g(x) = |x + 5|
g(-7) = |-7 + 5|
g(-7) = |-2|
g(-7) = 2
The solution is 2.
Example 3:
Evaluate the function: h(x) = x2 + 8 for h(4)
Solution:
h(4) means the variable x = 4. Substitute 4 into the equation for x, then simplify using PEMDAS.
h(x) = x2 + 8
h(4) = 42 + 8
h(4) = 16 + 8
h(4) = 24
The solution is 24.
Now you try an example. Enter the answer into the space provided to check your solution.
Evaluate the function: f(x) = 4x - 7 for f(5)
Example 2: Enter the answer into the space provided to check your solution.
Evaluate the function: h(x) = 3x2 + 5 for h(4)
Example 3: Enter the answer into the space provided to check your solution.
Evaluate the function: f(x) = 6 - 2x for f(5)
Example 4: Enter the answer into the space provided to check your solution.
Evaluate the function: f(x) = 4 + 2x2 for f(3)
*It is important to remember when evaluating functions you need to use PEMDAS in order to calculate the correct answer*