Spring 2006

Justify all answers with neat and organized work. Clearly indicate your answers. 20 points possible.

1. (5 pts.) Submit your take-home Geometer's Sketchpad problem by tomorrow.

2. (5 pts.) Let f(x)=2x+3x².

(a) Find f(x+h) and simplify.

(b) Find

f(x+h)-f(x) h

and simplify.

3. (5 pts.) Let f(x)=x²+x and g(x)=5x²+2x.

(a) Find the function f°g and simplify.

(b) Find the function g°g and simplify.

4. (5 pts.) 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 112 chirps per minute at 70^°F and 175 chirps per minute at 80^°F.

(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? What does it represent?

(c) If the crickets are chirping at 140 chirps per minute, estimate the temperature.