4. Consider the function b(x) defined on [−3,3] pictured below. Let c(x) denote the restriction of b(x) to [−3, −2] (that is c(x) is the part of the graph of b(x) on [−3, −2]), let d(x) denote the restriction of b(x) to [−1, 1], and let f(x) denote the restriction of b(x) to [1,3]. Which of the following statements are true? • The range of f-1 is [1,3]. • The domain of d-1 is contained in [-100, 50]. • The range of d-1 is con- tained in [−1,2]. • The domain of c−1 con- tains the range of b. • The range of b contains the range of c. • None of the statements are true. 50 y -3 2 -1 1 2 -50 -100 -150 -200

2. Let f(x)=x2x3 - 3. a) Find the domain of the function: ○ [-3,00) Ⓒ (-∞0, 3] (-∞0, 3) U (3, 0) (∞, -3) U (-3,00) b) Find the range of the function: (-∞0, 2) U (2,00) ○ [2,00) Ⓒ (-∞, -2] O (-∞, -2) U (-2, 0) c) Is f a one-to-one function? Yes, f is one-to-one. No, f is not one-to-one. d) Use your answer from part c to determine if the inverse of the function f is a function. Yes, the inverse of the function f is a function. No, the inverse of the function f is not a function.

2. If f(2) = e*, describe the images under f(z) of horizontal and vertical lines, i.e. what are the sets f(a + it) and f(t + ib), where a and b are constants and t runs through all real numbers?

4. Function f is defined by f(x) = 2x – 7 and g is defined by g(x) = 5*. a. Find f(3),f(2),f(1),f(0), and Find g(3), g(2),g(1), g(0), and b. f(- 1). 8(- 1). f (3) = 8 (3) = f (2) = 8 (2) = f(1) = 8 (1) = f (0) = 8 (0) = f(- 1) = 8(- 1) = (From Unit 1, Lesson 3.)

= mx + b. 4. Let m and b be real numbers, and consider the following three functions: f(x) = 2x + 1, g(x) x + 2, and h(x) A. If function f has a codomain of (5, 7) U (7, 9), the largest its domain can be chosen is (2, 3) U (3, 4). Explain. B. If function g has a codomain of (−1, 1) U (1, 3), the largest its domain can be chosen is (-3, 3) U (3, 9). Explain. C. Within the context of the e- definition of a limit, your result from part A suggests that if € is equal to 2, the largest that can be chosen for function f(x) is 1. Explain. =

2) a. Show that the function f(x) = A x x – B is injection function. b. Find the inverse of the function f (x) = -B × x + 5 x A Note that: A is first two-digit number (before English alphabet letter) from your college ID. B is last four-digit number (after English alphabet letter) from your college ID. For example, if your MEC ID is 16F234510, then A = 16 and B = 4510

2. Refer to the function p(x) = x². (a) Suppose r(x) = p(x+3)– 2. Describe how p(x) is transformed to create r(x). Verify your description by graphing using Desmos. (b) Suppose q(x) = -p(x – 1) + 7. Describe how p(x) is transformed to create q(x). Verify your description by graphing using Desmos. | (c) Suppose s(x) = -4p(3(x – 1)) – 2. Describe how p(x) is transformed to create s(x). Verify your description by graphing using Desmos. (d) Suppose u(x) is created by shifting p(x) 3 units to the left and 2 units down. Write u(x) in terms of p(x), and then find an algebraic expression for u(x). (e) Suppose v(x) is created by compressing p(x) horizontally by a factor of 2 and shifting 9 units up. Write v(x) in terms of p(x), and then find an algebraic expression for v(x).

1. Write the function in the form f(x) = a(x – h)² + k: a). f(x)= 2x -12x +11; b) y =-x² +x +:

6. Let r(x) = x² + 3x– 10 and s(x) = x – 2. Build a new function, 1(x), for which 1(x)=| x. State any restrictions on the domain and range.

2. Let m(x) = 2x² - ax - 2 and n(x) = bx² + 2x + 5. The functions are combined to form the new function p(x) = m(x)n(x). Points (1,-40) and (-1, 24) satisfy the new function. Determine m(x) and n(x). Leave the final answer in exact form.