1.1 - Functions

Ex. 1 Describe the sets of numbers using set- builder notation. a. {8,9,10,11,…}

Ex. 1 Describe the sets of numbers using set- builder notation. a. {8,9,10,11,…} {x|x > 8, x E W}

Ex. 1 Describe the sets of numbers using set- builder notation. a. {8,9,10,11,…} {x|x > 8, x E W} b. x < 7

Ex. 1 Describe the sets of numbers using set- builder notation. a. {8,9,10,11,…} {x|x > 8, x E W} b. x < 7 {x|x < 7, x E R}

Ex. 1 Describe the sets of numbers using set- builder notation. a. {8,9,10,11,…} {x|x > 8, x E W} b. x < 7 {x|x < 7, x E R} c. All multiples of three

Ex. 1 Describe the sets of numbers using set- builder notation. a. {8,9,10,11,…} {x|x > 8, x E W} b. x < 7 {x|x < 7, x E R} c. All multiples of three {x|x = 3n, n E R}

Ex. 2 Write each set of numbers using interval notation. a. -8 < x < 16

Ex. 2 Write each set of numbers using interval notation. a. -8 < x < 16 (-8,16]

Ex. 2 Write each set of numbers using interval notation. a. -8 < x < 16 (-8,16] b. x < 11

Ex. 2 Write each set of numbers using interval notation. a. -8 < x < 16 (-8,16] b. x < 11 (-∞, 11)

Ex. 2 Write each set of numbers using interval notation. a. -8 < x < 16 (-8,16] b. x < 11 (-∞, 11) c. x 5

Ex. 2 Write each set of numbers using interval notation. a. -8 < x < 16 (-8,16] b. x < 11 (-∞, 11) c. x 5 (-∞, 16] U (5, ∞)

Ex. 3 Determine whether each relation represents y as a function of x. a. He input value x is a student’s ID number and the output value y is that student’s score on a physics exam.

Ex. 3 Determine whether each relation represents y as a function of x. a. He input value x is a student’s ID number and the output value y is that student’s score on a physics exam. YES

Ex. 3 Determine whether each relation represents y as a function of x. a. He input value x is a student’s ID number and the output value y is that student’s score on a physics exam. YES b. Tables

c. Graphs d. y 2 – 2x = 5y – 2x 2 = 5

Ex. 4 Given f(x) = 3x – 5 and g(x) = x 2 + 2, find: (a) f(-3)

Ex. 4 Given f(x) = 3x – 5 and g(x) = x 2 + 2, find: (a) f(-3) f(x) = 3x – 5

Ex. 4 Given f(x) = 3x – 5 and g(x) = x 2 + 2, find: (a) f(-3) f(x) = 3x – 5 f(-3) = 3(-3) – 5

Ex. 4 Given f(x) = 3x – 5 and g(x) = x 2 + 2, find: (a) f(-3) f(x) = 3x – 5 f(-3) = 3(-3) – 5 = -9 – 5 = -14

Ex. 4 Given f(x) = 3x – 5 and g(x) = x 2 + 2, find: (a) f(-3) f(x) = 3x – 5 f(-3) = 3(-3) – 5 = -9 – 5 = -14 (b) g(2z)

Ex. 4 Given f(x) = 3x – 5 and g(x) = x 2 + 2, find: (a) f(-3) f(x) = 3x – 5 f(-3) = 3(-3) – 5 = -9 – 5 = -14 (b) g(2z) g(x) = x 2 + 2

Ex. 4 Given f(x) = 3x – 5 and g(x) = x 2 + 2, find: (a) f(-3) f(x) = 3x – 5 f(-3) = 3(-3) – 5 = -9 – 5 = -14 (b) g(2z) g(x) = x g(2z) = (2z) 2 + 2

Ex. 4 Given f(x) = 3x – 5 and g(x) = x 2 + 2, find: (a) f(-3) f(x) = 3x – 5 f(-3) = 3(-3) – 5 = -9 – 5 = -14 (b) g(2z) g(x) = x g(2z) = (2z) = (2) 2 (z) 2 + 2

Ex. 4 Given f(x) = 3x – 5 and g(x) = x 2 + 2, find: (a) f(-3) f(x) = 3x – 5 f(-3) = 3(-3) – 5 = -9 – 5 = -14 (b) g(2z) g(x) = x g(2z) = (2z) = (2) 2 (z) = 4z 2 + 2

Ex. 5 Identify the domain & range of each function. a. y = √ x + 4

Ex. 5 Identify the domain & range of each function. a. y = √ x + 4 x + 4 > 0

Ex. 5 Identify the domain & range of each function. a. y = √ x + 4 x + 4 > 0 x > -4

Ex. 5 Identify the domain & range of each function. a. y = √ x + 4 x + 4 > 0 x > -4 Domain: { x | x > -4}

Ex. 5 Identify the domain & range of each function. a. y = √ x + 4 x + 4 > 0 x > -4 Domain: { x | x > -4} b. f(x) = 2 + x x 2 – 7x

Ex. 5 Identify the domain & range of each function. a. y = √ x + 4 x + 4 > 0 x > -4 Domain: { x | x > -4} b. f(x) = 2 + x x 2 – 7x x 2 – 7x ≠ 0

Ex. 5 Identify the domain & range of each function. a. y = √ x + 4 x + 4 > 0 x > -4 Domain: { x | x > -4} b. f(x) = 2 + x x 2 – 7x x 2 – 7x ≠ 0 x(x – 7) ≠ 0

Ex. 5 Identify the domain & range of each function. a. y = √ x + 4 x + 4 > 0 x > -4 Domain: { x | x > -4} b. f(x) = 2 + x x 2 – 7x x 2 – 7x ≠ 0 x(x – 7) ≠ 0 x ≠ 0x ≠ 7

Ex. 5 Identify the domain & range of each function. a. y = √ x + 4 x + 4 > 0 x > -4 Domain: { x | x > -4} b. f(x) = 2 + x x 2 – 7x x 2 – 7x ≠ 0 x(x – 7) ≠ 0 x ≠ 0x ≠ 7 Domain: { x | x ≠ 0, x ≠ 7, x E R}