A+ Answers

1.   Biologists have noticed that the chirping rate of crickets of a certain species is related to temperature, and the relationship appears to be very nearly linear. A cricket produces 113 chirps per minute at 21ºC and 173 chirps per minute at 27ºC.

      (a) Find a linear equation that models the temperature T as a function of the number of chirps per minute N.

      (b) What is the slope of the graph and what does it represent?

      (c) What is the T-intercept of the graph and what does it represent?

      (d) If the crickets are chirping at 150 chirps per minute, estimate the temperature.

2.   Consider the piecewise function  

      (a) Sketch a graph of f.

      (b) State the domain and range of f.

      (c) Does f have an inverse? If not, explain why, otherwise if so then sketch the inverse function f^-1

3.   Find the domain of the function  

4.   Is the function given by  even or odd or neither? Please justify your reasoning.

5.   Factorize the quintic polynomial  into a product of irreducible linear and quadratic factors. What are the roots of P?

6.   Consider the rational function  

      (a) What is the domain of g?

      (b) Given that g is one-to-one, find the inverse g^-1.

      (c) What is the range of g?

7.   use partial fractions to simplify the rational function  

8.   Solve the equation  for 0 ≤ x ≤ 2π.