Questions from General Calculus

Q: If f(x) = x + 4 and h(

If f(x) = x + 4 and h(x) = 4x - 1, find a function g such that g 0 f = h.

Q: Suppose g is an even function and let h = f 0

Suppose g is an even function and let h = f 0 g. Is h always an even function?

Q: Suppose g is an odd function and let h = f 0

Suppose g is an odd function and let h = f 0 g. Is h always an odd function? What if f is odd? What if f is even?

Q: Suppose the graph off is given. Write equations for the graphs

Suppose the graph off is given. Write equations for the graphs that are obtained from the graph off as follows. a. Shift 3 units upward. b. Shift 3 units downward. c. Shift 3 units to the right. d...

Q: Explain how each graph is obtained from the graph of y =

Explain how each graph is obtained from the graph of y = f(x). a. y = f(x) + 8 b. y = f(x + 8) c. y = 8f(x) d. y = f(8x) e. y = -f(x) - 1 f. y = 8f(1/8 x)

Q: The graph of y = f(x) is given.

The graph of y = f(x) is given. Match each equation with its graph and give reasons for your choices. a. y = f(x - 4) b. y = f(x) + 3 c. y = 1/3 f(x) d. y = -f(x - 4) e. y = 2f(x + 6)

Q: The graph off is given. Draw the graphs of the following

The graph off is given. Draw the graphs of the following functions. a. y = f(x) - 3 b. y = f(x + 1) c. y = 1/2 f(x) d. y = -f (x)

Q: a. Write an equation that defines the exponential function with base

a. Write an equation that defines the exponential function with base b>0. b. What is the domain of this function? c. If b ≠ 1, what is the range of this function? d. Sketch the general shape of the...

Q: Sketch a rough graph of the market value of a new car

Sketch a rough graph of the market value of a new car as a function of time for a period of 20 years. Assume the car is well maintained.

Q: a. How is the number e defined? b.

a. How is the number e defined? b. What is an approximate value for e? c. What is the natural exponential function?