l. (3 pts) Convert to an exponential equation: log 4 .'t'= 5. Q explanation required] 1. A. 4x=5 B. 51:4 O. x4=5 D. x5==l E. 45=x F. 54:}; 2. (9 pts) Laura is a salesperson who must decide between two monthly income options. Option A: Salary of $EJ'TU' per month, plus 13% of monthly sales {in dollars) or Option B: Salary of $1?11 per month, plus 9% of monthly sales {in dollars) (a) State a linear mctionfr) that represents the Option A total income= give-n monthly sales ofx dollars. Eb} State a linear inction gfx} that represents the Option B total income, given monthly sales of x dollars. (of; Laura wants to determine the following: For what 31mm of monthly sales is Option A the better choice rather than Option B? To answer the question, should you solve the inequality f (x) 2 3113:) or the inequalityf (I) E gc}? Write the appropriate inequality, show how to solve it= and state your answer to the question in a sentence. 3. (9 pts) Letf(x) = x2 - 4x + 5 and g(x) = 3x + 5 (a) Find the composite function (f . g)(x) and simplify the results. Show work. (b) Find the composite function (g. )(x) and simplify the results. Show work. (c) Find (f g)(-2). Show work. 4. (8 pts) Let f(x) =- 4x2 -16 (no explanations required) (x +4x+3) (a) State the y-intercept. (b) State the x-intercept(s). (c) State the vertical asymptote(s). (d) State the horizontal asymptote.5. {10 pts) Let f9.) = hi T 43' 5 {a} Find f "I, the inverse functiongfg': Show work. (b) 'What is the domain 2:: 7 {c} 'What is the domain of the inverse rnction? 6. (11] pts) A box with no top is to be fashioned from a 45 inch by 21inch piece of cardboard by cutting out congruent squares 'om each corner of the cardboard and then folding the resulting tabs. Let 3: denote the length of the side of the square which is removed from each corner. {a} Find the volume V of the box as a function of x. Include an appropriate applied domain. (b) Using a graphing calculator or otherwise, approximate the dimensions of the box with maximum volume. 'What is the maximum volume? 7. (8 pts) Solve the equation. Check all proposed solutions. Show work in solving and state your final conclusion. x+4 2 = 0 x+3 x'+4x+3 8. (8 pts) Solve the equation. Check all proposed solutions. Show work in solving and state your final conclusion. x-7=14x-7 9. (9 pts) Let f (x) = e 2x-2. Answers can be stated without additional work/explanation. (a) Which describes how the graph of f can be obtained from the graph of y = e'? Choice: A. Stretch the graph of y= @ horizontally by a factor of 2 and right by 2 units. B. Shrink the graph of y = of horizontally by a factor of 1/2 and right by 2 units. C. Stretch the graph of y =e horizontally by a factor of 2 and right by 1 units. D. Shrink the graph of y = el horizontally by a factor of 1/2 and right by 1 units. (b) What is the y-intercept? State the approximation to 2 decimal places (i.e., the nearest hundredth). (c) Draw the graph of y = e and the graph of f(x) on the same graph.1|]. [1?" pts} On a particular fall day, the outdoor temperature was recorded m and a quadratic function was used to model the data. J: =i'} = 113:2 + 91?: 2 for 4 E ti: 22 where t = time of do}? [inhoursj and y = temperature (in degrees) REh-L-hRK: Time is measured in hours elapsed since midnight. For instance, 1' = 4 means 4 am. i'= 22 means 1!] pm. (a) Using algebraic m we hate learned, nd the maximum temperature predicted by the quadratic model and nd the time when it occurred. Report the time to the nearest half hour (Le.= _:I1]EI or _:3E|]-. {For instance. a time of 13.3 hours is reported as 6:30 pm in the usual time notation.) Report the maximum temperature to the nearest tenth of a degree. Show algebraic work. {b} Find and interpret the average rate of change n_f_fover the interval [-5, 12]. Show work. (of; Use the quadratic polynomial J: = 41.31.\"2 + 9.7": 2 together with algebra to approximate the time(s) of da'j,r when the outdoor temperature 1.: was fit] degrees. That is= solve the quadratic equation 6'0 = H.339 - 9.7: 2. Show work in solving. (Show hon.r the quadratic formula is used, with the appropriate values substituted.) Round the results to the nearest tenth. 1Write a concluding sentence to report the timefs] to the nearest halfhour, in the usual time notation. 11. (9 pts) Solve and graph f s |s Eu'l