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