Name______

These practice problems are IN ADDITION to your study guide on :Conics, Factorials, Combinations, Pascal’s Triangle, Binomial Expansion and Complete the square.

  1. Extrema are the ______and ______points of a function.
  1. The parent quadratic function has sections of both increasing and decreasing if the “a” is negative the parabola will ______.
  1. The parent logarithmic function grows ______and is always ______.
  1. All polynomial functions can be graphed as ______and ______curves.
  1. A ______is caused in the graph of a rational function when the same factored term appears in

both the numerator and denominator.

  1. The 4 conic sections are
  1. The only conic section that can be a function is ______

8.The hypotenuse of a 30-60-90 triangle is ______the length of the short leg.

9.The graph of a function and its inverse are reflections of each other across the ______line.

10.The hypotenuse of a 45-45-90 triangle is ______times the length of one leg.

11.The vertex of is at the point ______.

12.A logarithm is an ______.

13. Rewrite as a single logarithm.

14. The base of the common log is _____.

15.The base of the natural log is ______.

16.The value of the irrational number _____ is approximately 2.71828

17.log5 145 = x can be written in exponential form as

18.Which graph does not represent a function?

A. B. C. D.

19.What is the solution of the equation

20.List 2 points on the graph of the common log

21.List 2 points on the graph of . Then sketch.

22.List 2 points on the graph f (x) = 4x. Then,sketch this graph.

23.The inverse of an exponential function is a ______function.

24.Given an initial amount of 11,000 dollars to invest with continuous compounding of interest at 3.5%

annually. Determine the amount after 7 years.

25.Given a population of bacteria is dying at a rate of 22% per day. Given an initial population of 120 million, what is the population after 10 days?

26.Rewrite as a single logarithm

27.Simplify

28.Analyze the following function and select the correct description.

29.Use the change of base formula to find log5 145

30.Write a quadratic function equation stretched vertically by a factor of 4,

shifted right 3 units and up 2 units.

A. B. .

C. D.

31.If a polynomial equation has a degree of 7, how many complex roots does it have

32.Explain the transformations of the basic reciprocal function for

33.Solve the quadratic equation. Hint : put the terms in descending power order first!

34. Find all real zeros of the equation

35.Solve

36. Solve

37.Find the excluded value of the equation

38.Write the domain for #37

39.Is the excluded value (singularity) a hole or vertical asymptote in #37

40.Where does the graph of #37 cross the x axis?

41.Write the correct interval notation for a domain that includes all real numbers

42.Determine the x-intercepts of the quadratic function

43.Write the quadratic formula

44.Factor

45.Solve for x. Round to the nearest hundredth.

46.Write as a single logarithm?

47. Find the exact value of
48.Write as a single logarithm?
49. What is the solution of the equation log (5x) =2?
50. Which equation is for direct variation? _____
Which equation is for inverse variation? ______
  1. B. C.. D.

51.y varies directly with x. If y = -4 when x = 2, find y when x = -6.

  1. y varies inversely with x. If y = 40 when x = 16, find x when y = -5.
  1. List all real zeros, x-intercepts, roots of the following function:
  1. List the possible rational roots of the equation. Then, determine the actual rational root(s).
  1. Determine between which two consecutive integers the real zeros of the

function are located.

  1. vertical asymptote(s)

root(s)

Determine the equation of the line that represents the slant asymptote. (synthetic division)

  1. What is the equation of the axis of symmetry?
  1. A polynomial graph has 4 turns and the end behavior is

Degree ____, ______leading coefficient

  1. If the remainder is zero after dividing a polynomial by (x+3), select the true statement

_____ is a root of the polynomial. ______is a factor of the polynomial. The point ______is on the graph of the polynomial.

  1. Sketch the 4 possibilities for end behavior of a polynomial with the parity of the degree and sign of the leading coefficient.
  1. What is a rational number?
  1. Write an equation of least degree with the following roots: {0, 3,8, 7i}