Algebra Basics
Used to determine if a relation between quantities is a function.
What is the vertical line test?
The solution to
3x + 5 = 4 – 5x
What is
x=-1/8
The number of terms that appear in the expansion of
(x^3 – 3x)^12
What is 13
The definition of a logarithm.
log_b(x)=y -> b^y=x
Logarithms are the inverse of an exponential function for x>0
The value of tan((5pi)/4)
What is 1
The exact distance PQ between the points P(–3,2) and Q(8,3).
What is the
sqrt(122)?
This is used to find the number of solutions a quadratic could have
The discriminant
An infinite geometric sequence is said to _________ if it approaches a single value.
What is converge?
The name for a logarithm with a base equivalent to Euler's number
What is the natural logarithm?
The amplitude and period of f(x)=4sin(5x+pi/3)-2
What is 4 and (2pi)/5 ?
The set of numbers represented by the symbol ℚ
What is the set of all rational numbers?
A line that describes the behavior of a function as
x->+-infty
A horizontal asymptote
The common difference of an arithmetic sequence, where the 5th term is 27 and the 15th term is 63.
The simplified value of log_3(27) + log_3(1/9)
What is 1?
The value and direction of the phase shift of f(x)=4sin(5x+pi/3)-2
What is (pi)/15 to the left?
If
f(x)=x^2+26/x-5
then
f(4)
What is 17.5?
The asymptotes of
g(x)=(5x–2)/(4x+1)
What are
x=-1/4
y=5/4
The amount to the nearest cent in an account after 18 months if an investor deposits $1200 at 5.6% annual interest, compounded monthly (assume no deposits or withdrawals).
A=$1304.90
The value of x in the exponential equation
243^(3k)*27^(-k)=81
What is 1/3?
One of the identities for cos(2x)
What is 2cos^2(x)-1 or 1-2sin^2(x) or cos^2(x)-sin^2(x)
State the domain restriction of
g(x)=(3x–1)/(x+2)
What is
xne-2?
f(x)=kx^2+(k–8)x+k
k is this value for the above quadratic to have equal real roots
What is -8
The coefficient of x^18 in the expansion of (x³ – 3x)¹² .
What is
((12),(3))*(-3)^9
-4,330,260
The solution when x<6 for
log_4(x^2) - log_4(x−3) = 2
x=4
The solution set to 1-2sin^2(x)=0
What is (((2k+1)pi)/4) where kinZZ
or all odd factors of pi/4