2 12 tttILt () _3x2+12 . S 0 a e x = ( p l f x2_x_2 below. Justifg your responses for each part by showing work or writing a brief explanation. . Factor the numerator and denominator to help you answer each part a. (1 pt) Find the domain off(x). b. (1 pt) Find the vertical asymptote(s), if any. c. (1 pt) Find the horizontal asymptote{s), ifany. d. (2 pt) Does this function have any removable discontinuities? If so, where? Give your answer as an ordered pair. e. (2 pts) Find the xintercepts and yintercepts, if any. 42. a. Use Figure 3.16 to rank the quantities f (1), f (2), f (3) from smallest to largest. b. Confirm your answer by calculating the quantities using the formula, f(x) = 2e - 3x x. 8 f(x) 4 X 1 3 4 -4 -8 Figure 3.1646. The value of an automobile purchased in 2020 can be approximated by the function V(t) = 30(0.85), where t is the time, in years, from the date of purchase, and V(t) is the value, in thousands of dollars. a. Evaluate and interpret V(4), including units. b. Find an expression for V(t), including units. c. Evaluate and interpret V'(4), including units. d. Use V(t), V'(t), and any other considerations you think are relevant to write a paragraph in support of or in opposition to the following statement: "From a monetary point of view, it is best to keep this vehicle as long as possible."2. If f(x) = 2* . 3*, find f (x) two ways: by using the product rule and by using the fact that 2* . 3* = 6*. Do you get the same result?For Problems 34-39, let h(x) = f(x) . g(x), and k(x) = f(x)/g(x), and I(x) = g(x)/f(x). Use Figure 3.19 to estimate the derivatives. 3 3 f (x) g(x) -3 X 3 -3 X 3 -3 -3 Figure 3.19 Use a property of exponents (look them up if you need to) to help you nd the derivative of at) : 2x - 3". o a. my) :m(5)5m o b. papa-53 o c. my) :6-6" 0 d. my) : mama: