Questions 1
Question 1 (1 point)
The ordered pairs in the table below represent a linear function.
What is the slope of the function?
b
4

Which graph corresponds to the function f(x) = x2 + 4x – 1?

Prove (a) cosh2(x) − sinh2(x) = 1 and (b) 1 − tanh 2(x) = sech 2(x). solution (a) cosh2(x) − sinh2(x) = ex + e−x 2 2 − 2 = e2x + 2 + e−2x 4 − = 4 = . (b) we start with the identity proved in part (a): cosh2(x) − sinh2(x) = 1. if we divide both sides by cosh2(x), we get 1 − sinh2(x) cosh2(x) = 1 or 1 − tanh 2(x) = .

What is the effect on the graph of the function f(x) = x2 when f(x) is changed to f(x) − 4?