0. Functions

In Exercises 19–32, find the (a) domain and (b) range.

𝔂 = 4 sin ( 1 )

x

In Exercises 19–32, find the (a) domain and (b) range.

𝔂 = 2 + 3x² .

x² + 4

In Exercises 19–32, find the (a) domain and (b) range.

________

𝔂 = 5 - √ x² - 2x - 3

Suppose that f(x) and g(x) are polynomials in x. Can the graph of f(x)/g(x) have an asymptote if g(x) is never zero? Give reasons for your answer.

In Exercises 19–32, find the (a) domain and (b) range.

𝔂 = cos(x - 3) + 1

Average single-family home prices P (in thousands of dollars) in Sacramento, California, are shown in the accompanying figure from the beginning of 2006 through the end of 2015.

b. Estimate home prices at the end of

i) 2007 ii) 2012 iii) 2015

How does the graph of the catenary y = a cosh x/a change as a > 0 increases?

101–104. Proving identities Prove the following identities.

cosh (x + y) = cosh x cosh y + sinh x sinh y

61–62. Points of intersection and area

a. Sketch the graphs of the functions f and g and find the x-coordinate of the points at which they intersect.

f(x) = sech x, g(x) = tanh x; the region bounded by the graphs of f, g, and the y-axis