Aurora National High School
Aurora Zamboanga del Sur
Name: ___________________________________________Grade Level: ________________
Strand: ___________________________________________Date: ______________________
General Mathematics Quarter 1 – Module 2: Evaluating Functions Worksheet
Evaluating function is the process of determining the value of the function at the number
assigned to a given variable. Just like in evaluating algebraic expressions, to evaluate the function
you just need to do the following steps:
1. Replace each letter in the expression with the assigned value.
2. Perform the operations in the expression using the correct order of operations.
Example:
Let 𝑓(𝑥) = 3𝑥 + 4, find 𝑓(2).
Solution:
𝑓(2) = 3(2) + 4
Since 𝑥 = 2, we just replaced x by 2
𝑓(2) = 6 + 4
in the expression then add by 4.
𝑓(2) = 10
Learning Competency: The learner evaluates a function. (Code: M11GM-Ia-2)
Directions: Answer the following activities using a separate sheet of Yellow Pad.
Activity 1: True or False
Directions: Identify if the following solutions is True or False.
1 – 3: Let 𝑓(𝑥) = 2𝑥 + 1
______1. 𝑓(2) = 2(2) + 1
=4+1
=5
_______3. 𝑓(𝑦) = Does not Exist
______2. 𝑓(𝑥 + 𝑦) = 2(𝑥 + 𝑦) + 1
= 2𝑥 + 2𝑦 + 2
= 2𝑥 + 4
4 – 5: Let 𝑔(𝑥) = 𝑥 2 + 1
______4. 𝑔(5) = 52 + 1
= 25 + 1
= 26
_______5: 𝑔(𝑥 + 𝑦) = (𝑥 + 𝑦)2 + 1
= 𝑥 2 + 2𝑥𝑦 + 𝑦 2 + 1
Activity 2: Complete the solution
Directions: Evaluate the functions by filling up the missing parts of the solution.
1. 𝑓(𝑥) = 3𝑥 − 5, find 𝑓(4)
Solution:
𝑓(4) = ___________
𝑓(4) = 12 − 5
𝑓(4) = ___________
2. 𝑔(𝑥) = 2𝑥 − 3, find 𝑔(𝑥 + 1)
Solution:
𝑓(𝑥 + 1) = __________
𝑓(𝑥 + 1) = 2𝑥 + 2 − 3
𝑓(𝑥 + 1) = __________
3. 𝑓(𝑥) = 𝑥 2 + 1, find 𝑓(5)
Solution:
𝑓(5) = __________
𝑓(5) = __________
𝑓(5) = 26
4. 𝑓(𝑥) = 2𝑥 3 + 3, find 𝑓(𝑥 + 1)
Solution:
𝑓(𝑥 + 1) = 2(𝑥 + 1)3 + 3
𝑓(𝑥 + 1) = ___________
𝑓(𝑥 + 1) = ___________
𝑓(𝑥 + 1) = 2𝑥 3 + 6𝑥 2 + 6𝑥 + 5
5. 𝑔(𝑥) = 𝑥 3 − 𝑥 2 , find 𝑔(2𝑥 + 3)
Solution:
𝑔(2𝑥 + 3) = (2𝑥 + 3)3 − (2𝑥 + 3)2
𝑔(2𝑥 + 3) = __________________
𝑔(2𝑥 + 3) = __________________
Activity 3: Evaluation
Directions: Evaluate the following functions with solutions.
1.
2.
3.
4.
5.
Given 𝑓(𝑥) = 𝑥 + 1, find the value of the function if 𝑥 = 9.
Given 𝑔(𝑥) = 𝑥 2 + 9, find the value of 𝑔(8).
Given 𝑚(𝑥) = 𝑥 4 + 𝑥 3 + 𝑦, find the value of 𝑚(4).
Given 𝑓(𝑥) = 𝑥 3 + 10, find the value of 𝑓(𝑥 + 2).
Given 𝑟(𝑥) = 𝑥 5 , find the value of 𝑟(𝑥 + 𝑦).
𝑓(𝑥+ℎ)−𝑓(𝑥)
ℎ
this quantity is called Difference quotient. Specifically, the difference quotient is
used in the discussion of the rate of change, a fundamental concept in calculus.
Example: Find the difference quotient for the function 𝑓(𝑥) = 2𝑥 + 6.
Solution:
𝑓(𝑥) = 2𝑥 + 6
𝑓(𝑥 + ℎ) = 2(𝑥 + ℎ) + 6 = 2𝑥 + 2ℎ + 6
Since 𝑓(𝑥) and 𝑓(𝑥 + ℎ) is found, thus we substitute their values to the difference quotient
formula.
𝑓(𝑥+ℎ)−𝑓(𝑥)
ℎ
=
=
=
2𝑥 + 2ℎ + 6 − (2𝑥+6)
Note: We put a Parenthesis in 𝑓(𝑥) because
ℎ
2𝑥 + 2ℎ + 6 − 2𝑥 – 6
ℎ
2𝑥 + 2ℎ + 6 − 2𝑥 – 6
ℎ
of the subtraction of two functions.
=
2ℎ
ℎ
=2
Activity 4: Difference Quotient
𝑓(𝑥+ℎ)−𝑓(𝑥)
Find the value of
, when ℎ = 0 for each of the following functions and show your
ℎ
solutions. Take note that there are no undefined final answers. (Hint: Only substitute ℎ to 0
when you have no ℎ in the denominator of every terms.)
1. 𝑓(𝑥) = 2𝑥 + 1
2. 𝑓(𝑥) = 𝑥 2 − 𝑥
3. 𝑓(𝑥) = (𝑥 + 1)3
Reflection: What are your thoughts about this worksheet?
“Never give up on what you really want to do.” – Albert Einstein
Prepared by:
Geonel D. Cortes
SPST – 1