Warm-Up 1/27Evaluate each expression given the value of the variable.

1. 3y – 4, y = 2

2. 2b + 7, b = – 3

2

1

Rigor:You will learn how to identify and evaluate

functions and state their domains.

Relevance:You will be able to use functions to solve real

world problems.

1-1 Functions

Real Numbers

IrrationalRational

Integers

Wholes

Naturals

Set-builder Notation

Example 1: Describe the set of numbers using set-builder notation.

a. (8,9,10, 11, …)

b. x < 7

c. all multiples of three

{𝑥|𝑥≥ 8 , 𝑥∈𝕎 }

{𝑥|𝑥<7 ,𝑥∈ℝ }

{𝑥|𝑥=3𝑛 ,𝑛∈ℤ }

Interval Notation

Example 2: Write each set of numbers using interval notation.

a.

b. x < 11

c.

¿

(− ∞ ,11)

¿∪(5 , ∞)

Example 3: Determine whether each relation represents y as a function of x.

a. The input value x is a student’s ID number, and the output value y is that student’s score on a physics exam.

b.

c.

Represents y as a function of x.

x y

– 8 – 5

– 5 – 4

0 – 3

3 – 2

6 – 3

Represents y as a function of x.

𝑦 2=2 𝑥+5𝑦=±√2 𝑥+5  Does not represents y as a function of x.

Example 4: If g(x) = x2 + 8x – 24, find each function value.

a. g(6)

b. g(– 4x)

c. g(5c + 4)

g(6) = (6)2 + 8(6) – 24

g(6) = 36+ 48 – 24

g(6) = 60

g(– 4x) = (– 4x)2 + 8(– 4x) – 24

g(– 4x) = 16x2 – 32x – 24

g(5c + 4) = (5c + 4)2 + 8(5c + 4) – 24

g(5c + 4) = 25c2 + 40c + 16 + 40c + 32 – 24

g(5c + 4) = 25c2 + 80c + 24

Example 5: State the domains of each function.

a.

b.

𝑥2−7 𝑥≠ 0𝑥 (𝑥−7)≠ 0𝑥≠ 0 , 𝑥≠ 7

{𝑥|𝑥≠ 0 ,𝑥 ≠7 ,𝑥∈ℝ }

𝑡−5≥ 0𝑡≥ 5

{𝑡|𝑡≥ 5 ,𝑡∈ℝ }

(− ∞ ,0)∪(0 ,7)∪(7 ,∞)

¿

Example 6: Evaluate the piecewise-defined function.

a.

b.

𝑖𝑓 𝑥>68𝑖𝑓 66 ≤ 𝑥≤ 68𝑖𝑓 63<𝑥<66

h (67 )=3 𝑥− 132

h (67 )=3 (67 ) −132

h (67 )=69

h (72 )=2𝑥−66

h (72 )=2 (7 2 )− 66

h (7 2 )=78

√−1math!

1-1 Assignment: TX p9-10, 4-52 EOE