Exam 3: Functions and Graphs

Given the function f(x)= find: (a)the domain (b)f(0) (c)f(1) (d)f (e)f (f)f

Sketch a graph of f(x)= |x + 3|

The height of an object thrown in the air depends on the time since it has been thrown.For a particular situation the height in meters of an object after t seconds can be represented by h(t)= 20t - 4.9 . (a)What is the height of the object if the time is x seconds? (b)If the time is increased by 2 seconds,how much higher is the object? (c)How much higher is the object per second increase? (d)If the time is increased by h,how much higher is the object? (e)How much higher is the object per unit increase?

Use a graphing calculator to find all real roots of the given function.Round answers to two decimal places,if necessary:

Sketch a graph of f(x)=

Given the function G(x)= find: (a)the domain (b)G(0) (c)G(6) (d)G(-4) (e)G(-10)

Sketch a graph of f(x)= + 4

Determine the x- and y-intercepts of the graph of y = - 16.

A cylinder has a height that is 4 more than the diameter of its base. (a)Write the area of its circular base as a function of its radius. (b)Write the volume of the cylinder as a function of its radius. (c)Without simplifying,write the ratio of the area of the circular base and the volume of the cylinder as a function of the radius. (d)Simplify the function you wrote in c. (e)What kind of function is this? (f)What is its domain out of context? (g)What is its domain in the given context?

In November,Steve uses his credit cards to buy $30.00 of holiday gifts each week.After 8 weeks he begins saving $30.00 each week to pay his credit card bill.Graph the absolute-value function to represent the amount Steve has saved since he started buying holiday gifts over the appropriate domain.(Hint: Let purchases on credit cards represent negative savings.)

If f(t)= (t + ,then f(t - 3)=

If f(x)= 2x + 3 and g(x)= 3x - 2,find: (a)(f ∘ g)(x) (b)(g ∘ f)(x)

Determine whether or not the function is one-to-one: f(x)= 7x + 6

If f(x)= 4x + 5,then =

The Cobb-Douglas production function for a company is given by P = 20 where P is the monthly production value when k is the amount of the company's capital investment (in dollars per month)and l is the size of the labor force (in work hours per month).What is the production value when l = 1728 hours and k = $27,000 per month?

If f(x)= 2x - 1 and g(x)= 4x + 8,then g(f(x))=

Sketch a graph of f(x)= + 5