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

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• Compare:
• graph of 2^x with graph of 2 ^-x
• graph of exp(x)= e^x with graph of exp(-x)
• graph of 2^x+3 with graph of 2^x+3= 8*2^x
• graph of 3*2^x with graph of 2^3x=8^x
  
  
• Compare:
• graph of log₂(x) = lg(2,x) with graph of 2^x
• 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)

 
• 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