Analyze the function below. Which of the following is/are true? f(x) = 2 5x² x-2 as x→-5+, f (x) → ∞ as x→-5, f (x) → ∞ as x → 2¯‚ ƒ (x) → ∞ None of the above as x→ 2+, f (x) →→∞ as x→-5+, f (x) → ∞ as x2, f (x) →→∞

(1a) Let A = {1, 6, 12}, B = {0, 2, 12}. The following are all relations from A to B, but which are functions? Explain why or why not? f1 = {(1, 2),(6, 0),(12, 12)} f2 = {(1, 0),(1, 2),(6, 12),(12, 0)} f3 = {(1, 12),(6, 0)} f4 = {(1, 0),(6, 0),(12, 2)}   (1b) Let X = {a, b, c, x, y, z} and Y = {1, 2, 3, 4, 5, 6, 7, 8, 9}. Define a function f : X → Y to be: f = {(a, 2),(b, 3),(c, 7),(x, 9),(y, 4),(z, 8)}. Define a function g : Y → X to be: g = {(1, b),(2, c),(3, b),(4, a),(5, z),(6, z),(7, b),(8, x),(9, y)}. Determine the following: 1. The range of f. 2. The range of g. Do we have Rng(f) a proper subset of Codom(f)? What about for g?

Make a table of values for f(x) = f(x) 4 6 32 ANGE 8 10 8885 12 N 140 14 192 16 252 60 - 4 showing function values for x = 4, 6, 8,....

Which of the following relation is a one-to-one function? Write your answers on the space provided.. (a) {(0,0),(1.1),(2,8),(3,27),(4,64)}     (b) {(-2,4),(-1,1),(0,0),(1,1),(2,4)}     (c) {(0,4),(1,5),(2,6),(3,7),..(n,n+4),…}     (d) Height to student     (e) Person to telephone number     (f) Height to age     (g) Birthdate of a family member

The one-to-one functions g and h are defined as follows. g={(-8, -4), (-3, 6), (1, 9), (2, 1)} h(x) = 3x + 13 믐 Find the following. − 1 8 (1) 9 O X 13 h 1² ¹(x) = -2 1³ 3 n) oh) (-6) (n Example -1 Next X S

The one-to-one functions g and h are defined as follows. g={(-5, 8), (2, −7), (7, 4), (9, 7)} h(x)=3x+14 Find the following. -1 9 (7) = ] -1 11(x) = 0 -(9-)("..-") =

Graph both functions on one set of axes. f(x) = (³.)* and g(x): = 1.5X -4 -2 -2 y 6 4 2 y 6 4 2 2 2 g 4 4 X X -4 g -2 -2 y 6 4 2 y 6 4 2 2 2 L 4 4 X X

Suppose that f and g are both odd. Which of the following functions are even? ☐ y = f(x)g(x) f(x) y = 12g(x) y = f(x) = g(x) y = g(x) ¹3 Which of the following functions are odd? y = f(x)g(x) f(x) y = 12g(x) y = f(x) = g(x) y = g(x)¹3

Which of the following relations is not a function? I. {(1,1), (1,2), (2, 3)} II. {(1,1), (1, 2), (0, 2)} III. {(1,2), (2,3), (3, 3)} (a) I (b) II (c) III (d) I and II (e) II and III

For a function f(x) that is one-to-one, if f(6) = 12 , then what is f-(12) = ? 1 6 1 O 12 1 12