Polynomial Functions and Equations
Rational Functions
Trigonometry
Logs Category
Miscellanious
100
f(x)=x(x+1)(x-3) determine Degree: End Behaviour: x-intercepts: y-intercept:
Degree: 3 End Behaviour:Q3-Q1 x-intercepts: x=-1,0,3 y-intercept: y=0
100
True or False: A 'reciprocal' function is the 'opposite' of the given function
True
100
Find the EXACT radian measure in lowest terms: 200 degrees
200 x (pie/180) =200(pie)/180 =20(pie)/18 =10(pie)/9
100
Evaluate: log2(32)^1/3 Hint: use power law
1/3log2(32) 1/3Log2(2)^5 1/3x1x5 =5/3
100
f(x)=2/(x^2-2x-3) State: Range: Domain: Behaviour at the ends:
Range:YER, y>0, y<-0.5 Domain: XER, x cannot equal -1,3 Behaviour at the ends: x approaches +infinity, Y approaches 0 x approaches -infinity, Y approaches 0
200
Using remainder theorem find the remainder of: 3x^3-2x^2+x-5 divided by (x+2)
f(2)=3(-2)^3-2(-2)^2+(-2)-5 =-24-8-2-5 =-39
200
Find the characteristics of the function f(x)=x-3 Intercepts x and y: Interval where the graph is below x axis: Interval where the graph is above x axis: Point(s) where the y value is 1:
f(x)=x-3 Intercepts x and y: x int=3, y int=-3 Interval where the graph is below x axis:x<3 Interval where the graph is above x axis:x>3 Point(s) where the y value is 1:(4,1), (2,-1)
200
Express the following as a single trigonometric ratio: 4Sin^2(x/2)-4cos^2(x/2)
=-4cosx
200
Solve: 500=100(1.06)^t
500=100(1.06)^t log500=log106^t log500=tlog106 log500/log106=t t=1.33
200
A ferris wheel has a diameter of 20m centre of circle is 11m off the ground and makes a complete rotation in 30s. Find the: Amplitude: Vertical shift: Period: Minimum: Maximum: K Value:
Amplitude:Amp=Radius=10 Vertical shift: 11 Period: 30 seconds Minimum:1 Maximum:21 K Value: =2pie/30 =pie/15
300
True of False: While applying transformations off the equation F(x)=a[k(x-d)]^n+c the value 'a' is the vertical stretch/compression by a factor of 'a'
True
300
find the horizontal asymptote f(x)=3x/(x-5)
Horizontal asymptote at y=3
300
Express as a single trigonometric ratio: 5sin(3x)cos(3x)
5sin(3x)cos(3x) 5(2sin3xcos3x) let (3x) be A 5(2sinA) 5(2sin(3x)) 5/2sin6x
300
Solve for x: 7^x=6^x+3
7^x=6^x+3 log7^x=log6^x+3 xlog7=x+3log6 xlog7-xlog6=3log6 x(log7-log6)=3log6 x=3log6/log7-log6 x=34.87
300
Combining Functions: A company produces a product for $10.00 per unit, plus a fixed operating cost of $48000. The company sells the product for $12.90 per unit. 1) determine a function, c(x) to represent the cost of producing x units. 2)Determine a function, s(x) to represent sales of x units 3) Determine a function that represents profit
1)c(x)=48000+10n 2)s(x)=12.90n 3)P=R-C P=12.90n-(48000+10n) =12.90n-48000+10n P=22.90n-48000
400
Find the average rate of change of the function, f(x)=x^4+3x^2+7x-1 between XE[0,3]
f(3)=3^4+3(3)^2+7(3)-1 =81+27+21-1 =128 f(0)=0^4+3(0)^2+7(0)-1 =-1 Y2-Y1/X2-X1 =128-(-1)/3-0 =43
400
f(x)=x+3/4x-8 Find: Domain: Range: Equation of Vertical Asymptote: Equation of Horizontal Asymptote:
Domain: (-infinity, 2) (2, infinity) Range: (-infinity, 1/4) (1/4, infinity) Equation of Vertical Asymptote: x=2 Equation of Horizontal Asymptote: y=1/4
400
Simplify: cos(x)XTanx=sinx
cos(x)X(sinx/cosx)=sinx Ls=Rs
400
Solve: 3^x-2=5^x
3^x-2=5^x log3^x-2=log5^x (x-2)log3=xlog5 xlog3-2log3=xlog5 xlog3-xlog5=2log3 x(log3-log5)=2log3 x=2log3/(log3-log5)
400
Rational Functions: The number of houses in a new subdivision after t months is modelled by N(t)=100t^3/100+t^3, where N is the number of houses and 0
N(6)=100(6)^3/100+(6)^3 =68.35 N(0)=100(0)^3/100+(0)^3 =0 Y2-Y1/X2-X1 =68.35-0/6-0 =11.3917
500
Solving polynomial inequalities: Solve: x^3-5x^2+6x>0
x^3-5x^2+6x>0 =x(x^2-5x+6)>0 =x(x-3)(x-2)>0 x(x-3)(x-2)=0 x=0, x=2, x=3
500
Solve this rational equation: x-3/x^2+3x=1/x+3-x-5/x^2+3x
x-3/x(x+3)=(1/x+3)-(x-5)/x(x+3) x-3=x-x+5 x=8
500
Sin(A+B)=SinACosB+SinBCosA
let B=A Sin (2A)=SinACosB+SinBCosA 2SinACosA
500
Quotient law: Solve log5x=1+log5(x-1)
log5x=1+log5(x-1) log5x-log5(x-1)=1 log5(x/(x-1)=1 5^1=x/(x-1) 5(x-1)=x 5x-x=5 x=5/4 x>1
500
Find: y=4cos(0.5x+pie/2)-1 Vertical stretch: Period: Vertical Shift: Horizontal Shift:
Vertical stretch:4 (amplitude) Period: 2pie/0.5=4pie Vertical Shift:Down 1 Horizontal Shift: Left pie
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