Functions
Polynomials and Quadratics
Radical and Rational
Exponentials
Sequences and Series
100
Given the equation y =f(x), Describe the transformations to f(x) to produce g(x) = f(x −4) +1?
Right 4, Down 1
100
100
Explain why 813/4 equals 27
The denominator of the rational exponent represents the index of a root, and the 4th root of 81 is 3 and 33 is 27.
100
The population of bacteria, P(t), in hundreds, after t hours can be modeled by the function P(t)=37e0.0532t . Determine whether the population is increasing or decreasing over time. Explain your reasoning.
e0.0532>1, so P(t) is increasing.
100
Is the sequence arithmetic? If so, find the common difference. 11.1, 18.2, 25.3, 32.4
yes, 7.1
200
Find f-1(x) if f(x)= (x-3)3+1
y=Cbrt(x-1)+3
200
The roots of the equation x2+2x+5=0 are
x= -1+2i and x=-1-2i
200
What is the solution set to x=sqrt(3x+40)
x=8, x=-5, x=-5 is an extraneous solution.
200
The value of t in the equation 276-t =9t-1
t=4
200
A sequence is defined recursively by
a1 =−2
an =3an−1 +1
What is the value of a4?
−41
300
The hours of daylight, y, in Utica in days, x, from January 1, 2013 can be modeled by the equation y=3.06sin(0.017x-1.40)+12.23. How many hours of daylight, to the nearest tenth, does this model predict for February 14, 2013
10.4
300
Given i is the imaginary unit, (2- yi)2 in simplest form is
-y2-4yi+4
300
Given when x is not equal to 2, the expression (2x2+5x+8)/ (x+2) is equivalent to
2x+1+(6/x+2)
300
Stephanie found that the number of white-winged cross bills in an area can be represented by the formula C=550(1.08)t , where t represents the number of years since 2010. Which equation correctly represents the number of white-winged cross bills in terms of the monthly rate of population growth?
1) C=550(1.00643)t
2) C=550(1.00643)12t
3) C=550(1.00643) t/12
4) C=550(1.00643)t+12
C=550(1.00643)12t
300
What is the sum of the first 19 terms of the sequence 3,10,17,24,31,. . .?
1254
400
On the coordinate plane, sketch at graph of a cosine function with a midline at y = −2, an amplitude of 3, and a period of π/2 on the interval [0,2pi]. Label all important information!!
Max y=1 min y=-5 P=π/2 amp=3 mid=-2 freq=4
400
What is the remainder when 4x3−3x+3 is divided by x−2?
29
400
Julie averaged 85 on the first three tests of the semester in her mathematics class. If she scores 93 on each of the remaining tests, her average will be 90. Write an equation that could be used to determine how many tests, T, are left in the semester.
(255+93T)/(T+3) = 90
400
The solution of 87e0.3x=5918, to the nearest thousandth, is
14.066
400
At her job, Pat earns $25,000 the first year and receives a raise of $1000 each year. The explicit formula for the nth term of this sequence is
an = 25,000 + (n − 1)1000. Which rule best represents the equivalent recursive formula?
1) an =24,000+1000n
2) an =25,000+1000n
3) a1 =25,000
an = an−1 +1000
4) a1 =25,000
an = an+1 +1000
3) a1 =25,000
an = an−1 +1000
500
In the town of Skaneateles, New York, house prices since 2008 have changed based on the function H(t)=200,000(1.045)t , where t is the number of years since 2008 and H(t) is the median house price. Determine the average rate of change for the median house price in Skaneateles, from 2010 to 2018 to the nearest dollar per year. Describe answer in context.
$11524. From 2014-2018, the median house price increased $11524 per year on average
500
Factor the expression completely: (x-1)2 + 5(x-1)-6
(x+5)(x-2)
500
For which set of values of x is the algebraic expression (x2-4) / (x2-4x-12) undefined
x=6 x=-2, but x=-2 cancels out
500
If $5000 is put into a savings account that pays 3.5% interest compounded monthly, how much money, to the nearest ten cents, would be in that account after 6 years, assuming no money was added or withdrawn?
6166.50
500
A ball is dropped from a height of 32 feet. It bounces and rebounds 80% of the height from which it was falling. What is the total downward distance, in feet, the ball traveled up to the 12th bounce?
149