A FIRST COURSE IN MATHEMATICAL MODELING FINAL PAPER TESTED QUESTIONS WITH VERIFIED ANSWERS COMPLETE STUDY SHEET

A FIRST COURSE IN MATHEMATICAL
MODELING FINAL PAPER TESTED
QUESTIONS WITH VERIFIED ANSWERS
COMPLETE STUDY SHEET

●● piece wise defined functions
Answer: different equations over different values of x
eg: absolute value function


●● even function
Answer: ƒ(x) = ƒ(-x)
reflects about y-axis


●● odd function
Answer: ƒ(-x) = -ƒ(x)
reflects about x=y


●● domain
Answer: independent
D
eg: all of x

,●● range
Answer: dependent
E
eg: ƒ(x)


●● mathematical model
Answer: mathematical description (fn or equation) of a real-world
phenomenon, eg, popultion, demand, speed


not totally accurate, but an idealization. accurate enough to give useful
conclusions


●● empirical model
Answer: a best-fit curve based on observed data points
• linear regression


●● polynomial
Answer: powers are non-negative
• quadratic, cubic...


●● power functions

, Answer: polynomials w/ one term, or x with negative or fractional
power


●● root function
Answer: √x


●● inverse function
Answer: 1/x


●● rational functions
Answer: ratio of two polynomials: Q(x)/P(x)


●● algebraic functions
Answer: +, -, *, ÷, √, ^ of polynomials
• rational fns are algebraic


●● trigonometric functions
Answer: units of variables are in radians (not degrees)


sine and cosine are periodic
• cos(x+2π) = cos x