Logarithms
3
Growth, decay, or neither?
f(x) = -3(2)x
Neither because a is negative.
tanx =
cot x =
sin/cos
cos/sin
sin(pi/6)
1/2
Which quadrants apply to arcsine (or sin-1x)?
1st and 4th
Solve for x.
log10x=2
100
f(x) = 23x-1. For what value of x is f(x) = 1/16?
-1
1 + cot2x= ?
csc2x
tan(pi/4)
1
What is the 4th row of Pascal's triangle?
1 4 6 4 1
Simplify logarithms (if possible) and condense into one logarithm with base 3.
4log3x + log39 -7log3(x+2)
log3(x4)(2)/(x+2)7
If you are given a table and it is an exponential function, describe what would be true of the inputs and outputs.
Inputs: Changing additively
Outputs: Changing multiplicatively
sin(2x) =
2sinxcosx
cos(5pi/6)
-root3 /2
If a factor cancels completely from the numerator but not the denominator of a rational function, what feature does the function have?
Vertical asymptote
Write the end behavior as x increases without bound of the following function. Express your answer in the mathematical notation of a limit.
f(x) = lnx
lim x --> inf. f(x) = inf.
If you are given a residual plot with a clear exponential pattern, was the model appropriate?
No! Pattern = NOT appropriate
cos(a+b) =
cosacosb - sinasinb
sin(-11pi/6)
1/2
Where is the left end behavior going for f(x) = -5x3+2x2-11x
Positive infinity
Find the x-values of the point of intersection of the following functions within the domain.
f(x) = log3x - log34
g(x) = 2
36
A semi-log plot takes ______________ data and rescales it logarithmically to look _____________.
cos2x-sin2x=
cos(2x)
tan(2pi/3)
- root3
A sinusoidal function has a maximum at (4, 14) and a minimum at (12, -7). What is the period of the function?
16