Need help ASAP with my final 15 questions of this exam. Please read the instructions carefully and write the steps and solution.

MATH 107 -OL3 College Algebra Summer, 2019 Page 1 of 6 MATH 107 FINAL EXAMINATION – Part 2 This is an open -book exam. You may refer to your text and other course materials as you work on the exam, and you may use a calculator. You must complete the exam individually. Neither collaboration nor consultation with others is allowed. Record your answers and work on the separate answer sheet provided. There are 15 problems. Problems #1 –3 are Multiple Choice. (Work not required to be shown) Problems #4 -7 are Short Answer. (Work not required to be shown) Problems #8 -15 are Short Answer with work r equired to be shown. MULTIPLE CHOICE 1. Solve, and write the answer in interval notation: − 2 − 7 ≤ 0. A. (–, 2]  (7, ) B. (–, 2] C. [2, 7] D. [2, 7) 2. The graph of y = f (x) is shown at the left and the graph of y = g(x) is shown at the right. (No formulas are given.) What is the relationship between g(x) and f (x)? y = f (x) y = g(x) A. g(x) = f (x + 1) – 1 B. g(x) = f (x – 1) – 2 C. g(x) = f (x + 2) + 2 D. g(x) = f (x + 1) – 2 2 4 -2 -4 -2 -4 2 4 2 4 -2 -4 -2 -4 2 4 MATH 107 -OL3 College Algebra Summer, 2019 Page 2 of 6 3. Suppose that a function f has ex actly two x-intercepts. . Which of the following statements MUST be true? A. f is a quadratic function. B. There are two points on the graph of f which have x-coordinates of 0. C. f has exactly two real -number zero s. D. f is an invertible function. SHORT ANSWER (no work required) : 4. Judging graphs. (A) (B) (C) (D) There may be more than one answer for each part. If no graph qualifies, say “None” or “N/A.” (a) Which of these graphs (if any) represents a function? (b) Which of these graphs (if any) represents a one -to-one function? (c) Which of these graphs (if any) represents an even function? 5. Logarithms. (a) log 31 = ________ (fill in the blank) (b) Change the logarithmic statement = log 3(1 9) to an equivalent statement in exponential form. (c) State the numerical value of log 3(1 9) in simplest form. MATH 107 -OL3 College Algebra Summer, 2019 Page 3 of 6 6. A polynomial function is graphed below. (a) State the y-intercept. (b) State the zeros of the function . (c) On which intervals is the graph increasing? A. (–, – 4], [ – 2, –1], [3, ) B. [– 4, –1.5], [1.75, ) C. [–5, –2], [ –1, 3] D. [–9, ) (d) Which of the following is a polynomial function that might have the given graph? A. ()= 1 10 (− 3)(+ 1)(+ 2)(+ 5) B. ()= − 1 10 (− 3)(+ 1)(+ 2)(+ 5) C. ()= 1 10 (+ 3)(− 1)(− 2)(− 5) D. ()= − 1 10 (− 3)2(+ 1)(+ 2)(+ 5) MATH 107 -OL3 College Algebra Summer, 2019 Page 4 of 6 7. Let . (a) State the domain . (b) State the intercepts . (c) State the horizontal asymptote. (d) State the vertical asymptote(s). (e) Which of the following represents the graph of ? GRAPH A. GRAPH B. GRAPH C. GRAPH D. 2 18 () 5 x fx x − = − 2 18 () 5 x fx x − = − MATH 107 -OL3 College Algebra Summer, 2019 Page 5 of 6 SHORT ANSWER, with work required to be shown, as indicated . 8. A salesperson earns a base salary of $1, 22 0 per month and a commission of 4.4% on the amount of sales made. If the salesperson has a paycheck of $ 2,782 for one month, what was the amount of sales for the month? Show work. 9. Let f (x) = 5x2 – 2x – 8 and g(x) = 7 – 3x2. (a) Find the sum function ( f + g )(x) and simplify. (Work optional) (b) Evaluate the sum function f + g for x = – 1. That is, find ( f + g )( – 1). Show work. 10. Find the exact solutions and simplify as much as possible: 2x2 + 5 = 8x. Show work. 11. Donut Delights, Inc. has determined that when x donuts are ma de daily, the daily profit P (in dollars) is given by P(x) = –0.001 x2 + 2.7 x – 900 (a) What is the company’s daily profit if 1,000 donuts are made daily? Show work. (b) How many donuts should be made daily in order to maximize the company’s daily profit ? Show work. (c) What is the maximum daily profit ? Show work. 12. Solve the equation 6 5 + 2 − 3 = + 12 5 − 15 . Check your results. Show work. MATH 107 -OL3 College Algebra Summer, 2019 Page 6 of 6 13. Let f (x) = 3x2 + 7 and g(x) = x + 2. (a) Find the composite function ( f o g )(x) and simplify. Show work. (b) Evaluate the composite function f o g for x = – 4. That is, find ( f o g )( – 4). Show work. 14. The function ()= 4 − 1 5 is one -to-one. (a) Find a formula for the inverse function. Show work. (b) State the domain of the inverse function. 15. Note the continuous compounding formula : The amount A in an account after t years due to a principal P invested at an annual interest rate r (expressed as a decimal) , compounded continuously is A = Pe rt. Suppose $ 2,500 is invested in an account at an annual interest rate of 7. 7% compounded continuously. (a) For this scenario, state the numerical values for P and r. (b) How much money is in the account at the end of five years (rounded to the nearest dollar)? Show work. (c) How long (to the nea rest tenth of a year) will it take the investment to reach $ 5,000? Write an appropriate equation and show how to solve it.