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 21◦C and 173 chirps
per minute at 27◦C.
(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
2. Consider the piecewise function f(x) = ! (x − 1)2 if x > 1
tan x if −π
2 < x ≤ 0
(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 g(t) = 3
4. Is the function given by f(x) = (x − 5)(x + 5)x even or odd or neither?
Please justify your reasoning.
5. Factorize the quintic polynomial P(x) = x5 −x4 +7×3 −9×2 −18x into a
product of irreducible linear and quadratic factors. What are the roots of
6. Consider the rational function g(t) = t+3
(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 5x−1
8. Solve the equation 2 sin2 x − sin x = 1 for 0 ≤ x ≤ 2π.