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# College Algebra Study Guide

E.8

27. Show that each function is the inverse of the other: f(x) = 4x - 7 and .
Answer: Yes, the functions are inverse of each other. f(g(x)) = x and g(f(x)) = x.

28. Find the inverse of the function .
Answer: f -1(x) = x2 + 1 for x ≥ 0

29. Does the graph below represent a function that has inverse function? Answer: No, notice that horizontal lines can be drawn and intersect the graph more than once.

30. The formula is used to convert from x degrees Celsius to y degrees Fahrenheit.
Find the formula to convert from y degrees Fahrenheit to x degrees Celsius. Show that this formula
is the inverse function of f(x).
Answer: is the inverse, then , therefore the
formula is the inverse of f(x).

E.9

31. Graph the polynomial function: f(x) = 2x3-x2-13x-6. Indicate the graph's end behavior, the
x-intercepts, state whether the graph crosses the x-axis or touches the x-axis, indicate the y-intercepts.
If necessary, find a few additional points and graph the function.
Answer: The graph falls to the left and rises to the right, x = -2, , 3, y = -6. Crosses the
x-axis at every zero since each zero has multiplicity 1. 32. Graph the rational function . Indicate all x-intercepts, y-intercepts, horizontal asymp-
tote, vertical asymptote(s). If necessary, find a few additional points and graph the function.
Answer: x = 0, y = 0, vertical asymptote at x = 2, horizontal asymptote at y = 3. 33. Sketch the graph of the exponential function :
Answer: Horizontal asymptote located at y = -3 34. Graph the following Piecewise function and state the domain, range and intervals where the func-
tion is increasing, decreasing and constant. Answer: The domain of this function is the set of all Real Numbers, the range is the interval
[1,∞). The interval of increasing is (1,∞), the interval of decreasing is (-∞,-1) and the interval
where the function is constant is (-1, 1). See the graph below. E.10

35. Apply properties of Logarithms to simplify each expression. Answer: a) 25, 36. Expand each expression by writing in terms of sum or difference of logarithms. Answer: 37. Write the expression as a single Logarithm. Answer: 38. Write the expression as a single Logarithm. Answer: E.11

39. Suppose that y is such that . Evaluate Answer: 40. Solve for all the values of x that satisfy the equation: .
Answer: 41. Solve the equation by making an appropriate substitution, .
Answer: 42. Solve the radical equation. Check the proposed solutions. .

43. Find the rational zeros of f. List any irrational zero correct to two decimal places.

f(x) = x4 + 5x3 - 3x2 - 35x - 28.

Answer: Rational zeros: , Irrational zeros: 44. Solve the exponential equation. Round your answer to four decimal places. 45. Solve the radical equation. Check the proposed solutions. 46. Solve the exponential equation .