Logs
What is the base of a natural log?
e / Euler's number
How do you plot polar graphs (rad/x) (x/rad)
x/rad
Range for a sin graph
(1,-1)
Can there be an inverse of a quadratic function?
No, because they have the same output values for multiple input values
In what direction and how many units will this equation be shifted? x+2
2 to the left
Solve this logarithm (no calculators): Log3(27)= y
What is the first angle for r=3sin(2θ)
π/4
What is the frequency for this equation: 2sin(2(x+1))+10
1/π
What is the domain and range for an Arctan function?
Domain x=infinity, x=-infinity
Range: π/2, -π/2
What type of dilation is this, horizontal or vertical? 2x+4
Vertical dilation
What (x,y) point does every logarithmic graph pass through?
1,2
What type of Limacon is this graph (dented, looped,cardioid ): r=3+5 cos(θ)
Looped Limacon
What is Sin(2x) equal to?
2Sin(x)Cos(x)
Find the slant asymptote for this equation: 3x3-5x2+7/x2+2x-2
In a logarithmic function, every horizonal dilation is what?
A vertical translation
linearize this equation: F(x)=3*2x
log(y)=xlog(2)+log(3)
Where is the second peak for this equation: 3 sin (5θ)
π/2
What is the Arctan of (sqrt3/3)
π/6
What are the first 4 x asymptotes for the Secant equation from -2π to 2π?
x=3π/2, x=-π/, x=π/2, x=3π/2
All log function are what of each other?
Dilations of each other
simplify this equation into only one log: log(8x5)+log(x2)-9log(x)
log(8x7/x9)
Convert this cartesian plot into a polar plot: (2,4)
(you can leave your answer in r, tan-1)
sqrt(20),tan-1(4/2)
solve this equation so there is only tangent and sine left in the answer: 1-cos2x+1/sec2x
sin2x+1/tan2x+1 / (1)
On a white board please graph this equation: r=3+2cos(θ)
f(x)=3x2+18x+54, if you wanted to shift the equation 20 to the right, 5 up, and dilate the function by a factor of 1/3 , what would the equation look like
f(x)=(x-20)2+6(x-20)+59/3