The document explains the concept of functions in mathematics, including function notation and examples of evaluating various functions. It provides specific examples of calculating the output of functions based on given inputs and solving equations involving functions. Additionally, it touches on manipulating function expressions and includes a list of names, likely indicating contributors or examples.

1. A function is a ‘job’

2. The notation f(x) defines a function named
f. This is read as “y is a function of x.” The
letter x represents the input value, or
independent variable. The letter y is
replaced by f(x) and represents the output
value, or dependent variable.

3. x
You are familiar with function notation like:
y = 5x + 3 or y= x2 + 4x + 6
y = f(x) means that y is a function of x.
You read f(x) as ‘f of x’.
So, if y = x2 + 2, we can also write
f(x) = x2 + 2

4. If f(x) = 3x + 7, find:
(a) f(1) = 3(1) + 7
= 3 + 7
= 10
(b) f(4) = 3(4) + 7
= 12 + 7
= 19
(c) f(-2) = 3(-2) + 7
= -6 + 7
= 1

5. Let f(x) = 4x2 – 3, find:
(a) f(3) = 4(3)2 – 3
= 4(9) - 3
= 36 - 3
(b) f(-5)
= 33
= 4(-5)2 – 3
= 4(25) - 3
= 100 - 3
= 97

6. (1) Let f(x) = 7x – 8. Find the value of:
(a) f(2) (b) f(8) (c) f(-8)
(2) Let f(x) = 3x2 + 2. Find the value of each of these.
(a) f(4) (b) f(-1) (c) f(22)
(3) Let g(x) = 3x2 – 2x + 1. Find:
(a) g(3) (b) g(-2) (c) g(0)

7. If g(x) = 5x - 9, then:
(a) Solve g(x) = 21
⇒ 5x – 9 = 21
⇒ 5x = 30
⇒ x = 6
(b) Solve g(x) = -64
⇒ 5x - 9 = -64
⇒ 5x = -55
⇒ x = -11

8. If f(x) = x2 – 3x, then solve f(x) = 4.
⇒ x2 – 3x = 4
⇒ x2 – 3x – 4 = 0
⇒ (x - 4)(x + 1) = 0
⇒ (x - 4) = 0 or (x + 1) = 0
⇒ x = 4 or x = -1

9. (1) Let h(x) = 2x – 5. Solve h(x) = 7.
(2) Let g(x) = 4x - 3. Solve g(x) = 0.
(3) h(x) = x2 – 2
(a) Find h(3) and h(-6)
(b) Solve h(x) = 7
(4) Let f(x) = 3x2 – 11x.
(a) Find f(-3)
(b) Solve f(x) = 20

10. If h(x) = 2x + 7, then write an expression for:
(a) h(3x) = 2(3x) + 7
= 6x + 7
(c) 4h(x) = 4(2x + 7)
= 8x + 28
(b) 3h(x) = 3(2x + 7)
= 6x + 21

11. Let f(x) = x2 + 7, then write an expression for:
(a) f(x) +2 = (x2 + 7) + 2
= x2 + 9
(b) f(x + 2) = (x +2)2 + 7
= (x +2) (x +2) + 7
= x2 + 4x + 4 + 7
= x2 + 4x + 11

12. • AGUDA, Mark Clifford
• ALCANTRA, John Alfred
• ALTURA, Marjorie
• CASTRO, Danny
• DELA CRUZ, Christian James
• DELA CRUZ, Jerimie
• CORSINO, Brian
• FABRO, Cristine
• GADONG, Karl Said
• GAGTAN, Darlfred John
• GOROSPE, Christian
• HADAP, Karren Jae