Exam 3: Functions and Graphs

If f(x)= and g(x)= - 3x - 5,then the value of (f ∘ g)(4)is

The x- and y-intercepts of the graph of + = 1 are

Sketch the graph of f(x)= - 2x.Also determine the intercepts.

To encourage large group sales,a theater charges two rates.If your group is fewer than 10,each ticket costs $7.50.If your group is 10 or more,each ticket costs $7.00.Graph the compound function that represents the cost of buying N tickets.

Determine whether the graph of y = x - 2 is symmetric about the x-axis,the y-axis,the origin,or the line y = x.

The response R to a shock of intensity I is a number estimated by R = f(I)= . (a)Express f(2 )in terms of f( ). (b)What effect does the doubling of intensity have on response?

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.Write an absolute-value function to represent the amount Steve has saved since he started buying holiday gifts.(Hint: Let purchases on credit cards represent negative savings.)

If f(x)= + 1 and g(x)= x - 1,find (f ∘ g)(x)- (g ∘ f)(x)

; g(x)= 1 - 4x. Find: (a)f(0) (b)f(-1) (c)f(4)- f(-2) (d)f(g(0)) (e)g(f(0))

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

Suppose an artist always paints rectangular pictures using a square of unknown length as a reference.She always makes the length 4 units longer than the square,and the width is 2 units longer than the square. (a)Write a function l(x)for the length of a painting as a function of the length of the square. (b)Write a function a(x)for the area of a painting as a function of the length of the square. (c)Write a function (x)for the ratio of the length to the area as a function of the length of the square.

Determine whether or not the graph of y = is symmetric about the x-axis,the y-axis,the origin,or the line y = x.

To encourage conservation,a gas company charges two rates.You pay $0.53 per therm for 0-70 therms and $0.74 for each therm over 70.Write a compound fraction to represent the monthly cost of t therms of water.

The graph of y = is symmetric about the

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

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

If f(x)= ,find (a)f(-2) (b)f(0) (c)f (d)f(1) (e)f(5)

A shirt costs x wholesale.The price the store pays is given by the function s(x)= x + 5,where x is the wholesale price.The price the customer pays is c(x)= 2(x + 1)where x is the price the store pays.Write a composite function to find the customer's price as a function of the wholesale price.

If f(x)= - 2x + 3,find: (a)the domain (b)f(2) (c)f(-2) (d)f (e)f( ) (f)f(s + 1) (g)f(x + h)

Suppose f(x)= + 3xy - .Find f(y).