Need some assistance with the following problems:
College Algebra MATH 107 Summer, 2019, V1.8 SHORT ANSWER, with work required to be shown, as indicated. 22. Let f(x) - vx +5 and g(x) =x -3. (a) Find (-1). Show work. g (b) Find the domain of the quotient function -. Explain. 23. Points (1, 8) and (-7. 6) are endpoints of the diameter of a circle. (a) What is the length of the diameter? Give the exact answer, simplified as much as possible Show work. (b) What is the center point C of the circle? (c) Given the point C you found in part (b), state the point symmetric to C about the y-axis. e e W24. Find the equation for a line which passes through the points (9, -1) and (3, 5). Write the equation in slope-intercept form. Show work. 25. Alan, a resident of Metropolis, pays Metropolis an annual tax of $90 plus 1.8% of his annual income. If Alan paid $1.233 in tax, what was Alan's income? Show work. 26. Let f(x) =3x- + 4 and g(x) = x - 3. (a) Find the composite function (fog)(x) and simplify. Show work. (b) Find (fog )(-1). Show work. 27. Find the exact solutions and simplify as much as possible: 5x = 6x + 3. Show work. 28. Given the function f(x) =8+=x. find a formula for the inverse function. Show work.College Algebra MATH 107 Summer, 2019, V1.8 29. Donut Delights, Inc. has determined that when x donuts are made daily, the profit P (in dollars) is given by P(x) = -0.002 x- + 4.4x - 1500 (a) What is the company's profit if 800 donuts are made daily? (b) How many donuts should be made daily in order to maximize the company's profit? Show work. e WI8 / 11 (+ 100% College Algebra MATH 107 Summer, 2019, V1.8 20. Consider the polynomial P(x), shown in both standard form and factored form P(x) 1 4 _5 3-3x +-2x+6= =(x+3)(x+1)(x-2)(x-5) 5 (a) Which sketch illustrates the end behavior of the polynomial function? A. B D. Answer: (b) State the y-intercept Answer: (c) State the zeros of the function Answer: (d) State which graph below is the graph of P(x) Answer: in12. The graph of y =(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)? 12. H 2 2+ -4 -2 2 A -2 2 4 -27 -4- "- g(x) A g(3) =/(r- 3)-1 g() =/(x +1)-3 D g() -/6 -1)-17 / 11 100% - 18. Suppose $2,500 is invested in an account at an annual interest rate of 6.3% compounded continuously. How long (to the nearest tenth of a year) will it take the investment to double in size? Answer: 19. Let f (x) = x3 + 12x + 39. (a) Find the vertex. Answer: (b) State the range of the function. Answer: (c) On what interval is the function increasing? Answer: Page 7 of 11
