Parent Functions
Trig Identities
Exponential Functions
Logarithms
Parent Characteristics
100
What is the shape of a sine wave?
A continuous wave. A "roller coaster"
100
What is the tangent identity?
tanx= sinx/cosx
100
What is the parent exponential function formula?
f(x)=a
100
Which is the parent log formula?
y=logaX
100
How many points are needed on a graph?
5 points
200
What is the shape and period of a Cosine wave?
Shape: A "cup" shape Period: 2Pi/b
200
What uis the Law of Sines?
sinA/a = sinB/b =sinC/c
200
What is the parent exponential transformations formula?
f(x)=n(a)^(x+-h) +-k
200
What is the parent log transformations formula?
f(x)=loga(x+-h)+-k
200
What is the base is this equation? y=log(x+3)-2
The base=10
300
What is the reciprocal of a Cosine wave, and what is it's period and domain?
Reciprocal of Cosine: Secant Period: 2pi/b Domain: all real numbers except at the asymptotes
300
What is the Law of Cosines?
c^2=a^2+b^2-2ab(cosC) b^2=a^2+c^2(cosB) a^2=b^2+c^2-2bc(cosA)
300
Solve for x 8^(3x-4)=8^(5x+10)
x=-8
300
What is the multiplication log law?
Log(AB)=logaA+logaB
300
What is the base in this equation? f(x)=4^3
The base is 4
400
Which 2 Trigonometric have asymptotes at the beginning and end of the period?
Tangent and Cotangent
400
What are all the reciprocal identities?
sinx=1/cscx cscx=1/sinx cosx=1/secx secx=1/cos tanx=1/cotx cotx=1/tanx
400
Solve for 9^3x=81^(x-4)
x=-7
400
Convert Log7(49)=2 to exponential form.
7^2=49
400
What are the tranformations of this equation? f(x)= -2(4)^(x-3)+5
x-axis reflection HS= right 3 VS= up 5
500
Which 2 Trigonometric Functions have maximums and minimums between the asymptotes?
Secant and Cosecant
500
What are the Pythagorean Identities?
sin^2X+cos^2X=1 tan^2X+1=sec^2X cot^2X+1=csc^2X
500
Will this equation be an exponential growth or decay? f(x)=7(1/2)^x
decay, because the base is less than 1
500
Use the change of base equation to solve this problem. log16(32)
log2(32)/log2(16) =5/4
500
What are the transformations of this equation? Make an x, y table. f(x)= ln(x-2)+1
x y HS: right 2 2.5 .3 VS: up 1 3 1 Asymptote: x=2 4 1.7 4.5 1.9 5 2.1 8 2.8
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