Www.sanjac.edu



Cal 1 Boot Camp: Student PacketParent FunctionsParent FunctionGraphParent FunctionGraphLineary=xDomain: (-∞,∞)Range: (-∞,∞)Symmetry: Odd OriginAbsolute Valuey=IxIDomain: (-∞,∞)Range: [0,∞)Symmetry: Even Y-axisQuadraticy=x2Domain: (-∞,∞)Range: [0,∞)Symmetry: Even Y-axisRadicaly=xDomain: [0,∞)Range: [0,∞)Symmetry: NeitherCubicy=x3Domain: (-∞,∞)Range: (-∞,∞)Symmetry: Odd OriginCube Rooty=3xDomain: (-∞,∞)Range: (-∞,∞)Symmetry: Odd OriginExponentialy=bx, b>1Domain: (-∞,∞)Range: (0,∞)Symmetry: NeitherLogy=logbx, b>1, x>0Domain: (0,∞)Range: (-∞,∞)Symmetry: NeitherRational(Inverse)y=1/xDomain: (-∞,0)U(0,∞)Range: (-∞,0)U(0,∞)Symmetry: Odd OriginRational(InverseSquared)y=1/ x2Domain: (-∞,0)U(0,∞)Range: (0,∞)Symmetry: Even Y-axisGreatest Integery=int(x)=[x]Domain: (-∞,∞)Range:{y:yεZ}(integers)Symmetry: NeitherConstanty=C (in this graph y=2)Domain: (-∞,∞)Range: {y: y=C}Symmetry: Even Y-axisTips and Tricks - Transformations of Functionsy=mx+vy=ax-h2+vy=ax-h+vy=ax-h3+vy=a3x-h+vy=ax-h+vy=a?x-h+vy=a2x-h+vy=alog10x-h+vy=ax-h+vy=a(x-h)2+vTips and Tricks – Vertical Asymptotes and Horizontal Asymptotesfx=1x fx=1x-1fx=x2x-1Tips and Tricks – For x and y Intercepts, Vertical Asymptotes, and Horizontal Asymptotesy=x+1y=x2+3y=x3+6y=xy=x-9y=3xy=3x+10y=1xy=1x-1y=1x2y=1x+42y=1xy=1x-8Tips and Tricks – Determining the Following for GraphsUse the graph of f to determine each of the following. Where applicable, use interval notation:The domain of fThe range of fThe x-interceptsThe y-interceptIntervals on which f is increasingIntervals on which f is decreasingIntervals on which f is constantThe number at which f has a relative minimumThe relative minimum of ff(-3)the values of x for which f(x)=-2Is f even, odd, or neither?Understanding Graphs and Limitslimx→11x-12limx→1--1x-1limx→1+-1x-1limx→-2-x2+2x-8x2-4limx→-2+x2+2x-8x2-4Understanding Cal 1 GraphsWhere is the graph undefined, continuous, or discontinuous?f-2=f-1=f1=f2=x→1-=x→1+=x→-4+=x→∞-=f-2=limx→-2fx= f0=limx→0fxf2=limx→2fx=f4=limx→4-fx=limx→4+fx=limx→4fx=f1=limx→1fx=f4=limx→4fx=Definition of a DerivativeDefinition of a Derivative of a function:The derivative of f at x is given byf ’(x) = limΔx→0fx+Δx-fxΔxprovided the limit exists. For all x for which this limit exists, f ’ is a function of x.Find the limit by the limit process.fx=4xfx=x2-4x+7fx=7fx=x3 Tips and Tricks – Difference QuotientDefinition of a Difference Quotient:The expressionfx+h-fxhFor h ≠ 0 is called the difference quotient.For fx=4x , find fx+h-fxhFor fx=x2-4x+7 , find fx+h-fxhFor fx=1x-2 , find fx+h-fxhFor f(x)=x +8, find fx+h-fxhTips and Tricks -For Deriving Pythagorean Identitiessin2θ+cos2θ=1 tan2θ=sec2θ-1cot2θ=csc2θ-1Where did π come from?π=Cd-54292550355500Trigonometric Parent Functions-61912521844000-62865028575000Blank Unit CircleTips and Tricks – Do’s and Don’ts of Calculator:The Do’s:Texas Instruments TI - 84 Plus CE: Casio FX-115 ES Plus: Best Software Calculator!!!TI SmartView CE for the TI – 84 Plus Family:The Don’ts:Texas Instruments TI-83 series calculatorsTexas Instruments TI-30 series calculatorsTexas Instruments TI-nSpire calculatorsCasio FX-9750 GII calculatorCasio G series calculatorsBasic Differential Rules-53340052133500-72390079946500Basica Integration Formulas-90487531623000Formula Trig Sheet ................
................

In order to avoid copyright disputes, this page is only a partial summary.

Google Online Preview   Download