The document discusses functions, including: 1. A function relates an input to an output, and the product of two functions f and g is defined as f(x) * g(x) with domain Df intersect Dg. 2. The quotient of two functions f and g, excluding values where g(x) is zero, is defined as f(x) / g(x). 3. The composite function of f and g is defined as f(g(x)).

2. A function relates an input
to an output.
What is a Function?

3. If f and g are functions with domains 𝐷𝑓
and 𝐷𝑔, respectively, their product is the
function defined by
𝑓 ∙ 𝑔 𝑥 = 𝑓 𝑥 ∙ 𝑔 𝑥
The domain of 𝑓 ∙ 𝑔 𝑥 𝑖𝑠 𝐷𝑓⋂𝐷𝑔.
Product of Functions

4. Let f x = 5x, 𝑔 x = 2x + 1, and h x =
1
2
𝑥 + 10
Find the product of the following.
1. 𝑓 ⋅ 𝑔 𝑥
2. 𝑔 ⋅ 𝑔 𝑥
3. ℎ ⋅ 𝑓 𝑥
Example

5. If f and g are functions with domains 𝐷𝑓
and 𝐷𝑔, respectively, excluding the values
that make g(x) zero, then, their quotient
is the function defined by
𝑓
𝑞
𝑥 =
𝑓 𝑥
𝑔 𝑥
.
Quotient of Functions

6. Let f x = 5𝑥2
, 𝑔 x = 10𝑥3
+ x, and h x = 𝑥4
+
12
Find the quotient of the following.
1. 𝑓/𝑔 𝑥
2. 𝑔/𝑔 𝑥
3. ℎ/𝑓 𝑥
Example

7. If f and g are functions with domains 𝐷𝑓
and 𝐷𝑔, the composite function of f and g
is defined as
𝑓 ∘ 𝑔 𝑥 = 𝑓 𝑔(𝑥)
Composition of function

8. Let f x = 5𝑥2
, 𝑔 x = 10𝑥3
+ x, and h x = 𝑥4
+
12
Find the quotient of the following.
1. 𝑓 ∘ 𝑔 𝑥
2. 𝑔 ∘ 𝑔 𝑥
3. ℎ ∘ 𝑓 𝑥
Example

9. Finding the Domain

10. FAMOUS NUMBER
Think of “FAMOUS NUMBER”,
numbers that are used in movie
titles, books, computer games, etc.
The most numbers listed in a group
will be declared a winner.

11. “In other words…”
ACTIVITY 1:

12. “Match me up!”
ACTIVITY 2:

13. How each mathematical phrases be
translated into mathematical expression
and vice versa?
What are the common errors in writing
algebraic expression and vice versa?
GUIDE QUESTION

14. Make a list of algebraic expressions
for at least 5 and translate each into
verbal phrases.
EXERCISE:

15. A. Translate the following into mathematical
expressions.
1. Three times a number a minus four
___________________
2. A number c increased by 6
_____________________
QUIZ:

16. B. Translate each mathematical
expressions into verbal phrase.
1. 𝟓𝐱 − 𝟒
______________________________________
________________
2. 3(𝐱 + 6)
QUIZ:

17. A. Write 5 mathematical expressions and
translate it in at least two ways
B. When will be expression “the sum of the
squares of two number” and square of the
sum of two numbers have the same value?
ASSIGNMENT: