Math 115  Lab   M. Flashman
Graphs of Exponential, Logarithmic and Trignometric Functions

• Compare:
• graph of 2x with graph of 2 -x
• graph of exp(x)= ex with graph of exp(-x)
• graph of 2x+3 with graph of 2x+3= 8*2x
• graph of 3*2x with graph of 23x=8x

• Compare:
• graph of log2(x) = lg(2,x) with graph of 2x
• graph of ln(x) with graph of exp(x)
• graph of ln(x+3) with graph of ln(x) + 3 and ln(x) + ln(3)
• graph of ln (3x) with graph of 3ln(x),   ln(3)* ln(x) and ln(3) + ln(x)

• Compare:
• graph of sin(x) with graph of sin(-x)
• graph of cos(x) with graph of cos(-x)
• graph of sin(x) with graph of sin(x+2pi)
• graph of cos(x) with graph of cos(x+2pi)

• Graphs of sine Discuss how each constant  A, B, and C effects the graph.[>1, >0, <0.]
• 10-21 f(x)= Asin(x) Use animator; family
• f(x)= sin(Bx) Use animator; family.  See graph SinAX
• f(x)= sin(x+C) Use animator; family
• f(x)= Asin(Bx+C) Use animator; family. See  graph A sin(BX+C)

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• Graphs of cosine Discuss how each constant  A, B, and C effects the graph.[>1, >0, <0.]
• f(x)= Acos(x) Use animator; family
• f(x)= cos(Bx) Use animator; family
• f(x)= cos(x+C) Use animator; family
• f(x)= Acos(Bx+C) Use animator; family.

• Graphs of tangent Discuss how each constant  A, B, and C effects the graph.[>1, >0, <0.]
• f(x)= Atan(x) Use animator; family
• f(x)= tan(Bx) Use animator; family
• f(x)= tan(x+C) Use animator; family
• f(x)= Atan(Bx+C) Use animator; family
• Solving equations
• Find A and B if y=Acos(Bx) with y(0)=20, y(pi/2)=20. Are these unique?
• Find x if  3sin(x) + 2cos(3x) = 4 ; slider, table, solver