This document provides information about evaluating functions at given input values: 1) To evaluate a function means to find the output value f(x) given a specific input x. 2) The steps to evaluate a function are: 1) write the function, 2) substitute the input value for x, 3) perform the operations, 4) simplify. 3) Examples are provided to demonstrate evaluating various functions at different input values using the steps outlined. Exercises and homework problems are included for practice evaluating additional functions.

1. EVALUATING FUNCTIONS

2. INTRODUCTION
How large is the value of the output y in
the function y = 5x2 – 1 if we input x = 10?
If the radius of a spherical container is
12 cm, and can be calculated by using the
formula V =
4
3
𝜋𝑟3
. What is the volume of the
container?

3. ACTIVITY: GEAR UP!
Evaluate the following algebraic expressions,
given that x = -3, y = 2, and z = -8.
1. xy + z
2. 3xy
3. 4x – 2y – 5z
4.
3𝑦𝑧
𝑥
5. 10z + 4xy – 12

4. LEARNING OUTCOME(S):
•Find the value of a function given a
particular element of the domain; and
•Solve problems involving functions.

5. EVALUATING A FUNCTION
To evaluate a function, means to find
the value of the output f(x), given the input
x.

6. STEPS IN EVALUATING FUNCTION
1.Write the function.
2.Substitute the value of x in the given
function.
3.Perform the indicated operation.
4.Simply.

7. EXAMPLE 1
If x = 5 evaluate f(x) = 4x2 – 5x + 3.
SOLUTION:
Step 1: f(x) = 4x2 – 5x + 3
Step 2: f(5) = 4(5)2 – 5(5) + 3
Step 3: f(5) = 4(25) – 25 + 3
f(5) = 100 – 22
Step 4: f(5) = 78

8. EXAMPLE 2
If f(x) = 4x2 – 5x + 3, evaluate the following:
1. x = ¼
2. x = 0
3. x =
2
2
4. x + 1

9. EXERCISE: Firm Up!
Evaluate the following functions at x = -2.
1. f(x) = 4x2 – 6x + 7
2. f(x) =
𝑥 −4
2𝑥 −5
3. f(x) =
4𝑥 −5
𝑥+6
4. f(x) = 5x3 – 2x2 + 4x – 7
5. f(x) =
𝑥2 −4𝑥
𝑥 −4

10. SEATWORK: Check What You Know
Evaluate the following.
1. How large is the value of the output y in
the function y = 5x2 – 1 if we input x = 10?
2. If the radius of the container is 12 cm,
what is the volume of the container if
the volume can be calculated by using
the formula V =
4
3
𝜋𝑟3
?

11. GENERALIZATION:
• What does it mean to evaluate a function?
To evaluate a function, means to find the value of the
output f(x), given the input x.
• What are the steps in evaluating function?
1. Write the function.
2. Substitute the value of x in the given function.
3. Perform the indicated operation.
4. Simply.

12. EVALUATION: Deepen Your Understanding
If f(x) =
1
6𝑥 −3
, g(x) = 𝑥3
− 29 , and h(x) =
(5x – 3)(x + 1), evaluate the following:
1.f
1
12
4. h(-1)
2.h(0) 5. f(-10)
3.g(-3)

13. HOMEWORK: Challenge Yourself
Evaluate the following polynomial functions
for the given value of x.
1. f(x) = x4 – 4x3 + 3x2 – 5x – 1 ; x = -2
2. f(x) = 3x5 + 2x + 10 ; x = 1
3. f(x) = 2x3 – 7x2 + 9x ; x = -3
4. f(x) = x3 – 3x3 + x – 5 ; x = -
3
5
5. f(x) = 4x5 – x3 + 5x2 +
3
2
x -
1
2
; x = 3

14. Thank you