Exam 3: Functions and Graphs

Brett rented a bike from a rental shop and rode at a constant rate of 12 mph for 2.5 hours along a bike path,and then returned along the same path at the same rate.Write an absolute-value function to represent Brett's distance from the rental shop as a function of time.

Find the x-intercepts and the y-intercepts of y =

Ellen's health plan has a $10.00 copayment for complete pregnancy care.Let x represent the number of prenatal visits and y represent her cost for the pregnancy.Write an equation which represents the relationship between her cost for the pregnancy and her number of prenatal visits; describe the graph of this equation,and identify the intercepts.

Determine the x-and y-intercepts,if they exist,of the graph of - = 1.Also determine whether the graph is symmetric about the x-axis,the y-axis,the origin,or the line y = x.

To reduce inventory,a department store charges three rates.If you buy 0-5 pairs of socks,the price is $3.50 per pair of socks.If you buy 6-10 pairs of socks,the price is $3.00 per pair.If you buy more than 10,the price is $2.75 per pair.Graph the compound function that represents the cost of buying N pairs of socks.

A rectangular sheet of metal has a length that is 4 more than the width. (a)Write the area of the rectangular sheet as a function of the width. (b)Without simplifying,write the ratio of the length of the sheet to the area of the sheet as a function of the width. (c)Simplify the function you wrote in b. (d)What kind of function is this? (e)What is its domain out of context? (f)What is its domain in the given context?

If f(x)= and g(x)= + 5,find: (a)f(g(x))and (b)g(f(x)).

If f(x)= , (a)find the domain of f(x) (b)find f(3)

Determine whether the graph of - xy = 1 is symmetric about the x-axis,the y-axis,the origin,or the line y = x.

Suppose the area of a square tablecloth is t(x)= (x + .Express as a composition of two functions and explain what each function represents.

Sketch a graph of f(x)= + 7

If f(x)= 4 + 6x,find f(3s).

Sketch the graph of ,and give the domain and range.

Sketch a graph of f(x)=

Sketch a graph of f(x)=

Which graphs below represent functions of x? (a) (b) (c)

If h(x)= (2x - ,find functions f and g such that h(x)= f(g(x)).

If f(x)= 3 - 2x and g(x)= + 7,find: (a)(f ∘ g)(x) (b)(g ∘ f)(x)

Find the domain of the function: f(x)=

If f(x)= 7,find f(14).