Find a linear equation that models the temperature T as a function

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?

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

temperature.

2. Consider the piecewise function f(x) = ! (x ? 1)2 if x > 1

tan x if ??

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 ?t2 ?7t . 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 P? 1 6. Consider the rational function g(t) = t+3 2t?4 . (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?