Download The function f(x) = - (x - 3)2 + 4 has a critical point at x = 3

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.
2.
The parent quadratic function has sections of both increasing and decreasing if the “a” is negative the parabola will
__________________________________.
3.
The parent logarithmic function grows ____________ and is always _____________.
4.
All polynomial functions can be graphed as _____________ and _____________ curves.
5.
A ____________ is caused in the graph of a rational function when the same factored term appears in
both the numerator and denominator.
6.
The 4 conic sections are
7.
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 y   x  5  3 is at the point ____________.
12.
A logarithm is an ________________.
13.
Rewrite as a single logarithm. log 7  log 3
2
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
18.
Which graph does not represent a function?
A.
can be written in exponential form as
B.
C.
4 x2  2
19.
What is the solution of the equation
20.
List 2 points on the graph of the common log
D.
y  log 4 x . Then sketch.
21.
List 2 points on the graph of
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 log( 12)  log( 2) as a single logarithm
27.
Simplify log( 10)  ln e
28.
Analyze the following function and select the correct description.
y
( x  3)( x  7)( x  4)
( x  5)( x 2  9)
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.
1
( x  2) 3  3
4
3
C. y  4( x  3)  2
A. y 
B. . y 
D.
1
( x  3) 3  2
4
y  4( x  3) 3  2
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
f ( x) 
33.
1
3
( x  5)
Solve the quadratic equation. Hint : put the terms in descending power order first!
34.
Find all real zeros of the equation y  ( x  8)( x  10) x
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.
x5 7
Determine the x-intercepts of the quadratic function
y  x 2  2 x  15
43.
Write the quadratic formula
44.
Factor x  36
2
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? ______
A.
y  kx
B. y  k
C..
y
k
x
D.
y  x
51. y varies directly with x. If y = -4 when x = 2, find y when x = -6.
52. y varies inversely with x. If y = 40 when x = 16, find x when y = -5.
53. List all real zeros, x-intercepts, roots of the following function:
( x  5)( x  1)( x  3)(3x  2)  0
54. List the possible rational roots of the equation. Then, determine the actual rational root(s). x  2 x  5 x  6  0
3
2
55. Determine between which two consecutive integers the real zeros of the
function are located.
56. y 
( x  3)( x  7)
x5
f ( x)  1.45x 3  2 x 2  10
vertical asymptote(s)
root(s)
Determine the equation of the line that represents the slant asymptote. (synthetic division)
57. What is the equation of the axis of symmetry?
y  ( x  2) 2  9
x  , y  
58. A polynomial graph has 4 turns and the end behavior is
x  , y  
Degree ____, ________ leading coefficient
59. 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.
60. Sketch the 4 possibilities for end behavior of a polynomial with the parity of the degree and sign of the leading coefficient.
61. What is a rational number?
62. Write an equation of least degree with the following roots: {0, 3,8, 7i}