Exam 3: Functions and Graphs

The speed you must travel for a given amount of time depends on the distance you must cover. (a)Write a function r(d)for the speed if the time is 5 hours and the distance covered is d. (b)What is the domain of this function out of context? (c)What is the domain of this function in the given context? (d)Find r(x),r and r ,. (e)What happens to the speed if the distance is reduced (divided)by a constant c? Describe using an equation.

If g(x)= , (a)g(-3) (b)g(0) (c)g(4)

For the graph of y = , (a)Determine the intercepts. (b)Determine whether the graph is symmetric about the x-axis,the y-axis,the origin,or the line y = x. (c)Sketch the graph.(d)Based on your graph,is y a function of x? If so,state (e)the domain and (f)the range.

If f(x)= 2x + 3 and g(x)= - 4x - 2,find: (a)(f + g)(x) (b)(f - g)(x) (c)(fg)(x) (d) (x) (e)f(g(x)) (f)g(f(x)) (g)f(g(1)) (h)g(f(1))

If f(x,y,z)= ,find f(1,2,-3).

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

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

If f(x)= 4x - 5 and g(x)= + 3x - 1,then f(g(x))=

Determine: (a)5!; (b)

If f(x)= - 3x + 4,then f (2 + h)- f(2)=

Traci earns $15.00 per hour and Rich earns $18.00 per hour. (a)Write a function t(x)for Traci's earnings as a function of hours worked. (b)Write a function r(x)for Rich's earnings as a function of hours worked. (c)Assuming they work the same number of hours each week,write a function (t + r)(x)for their combined earnings as a function of hours worked.

Given the function f(x)= find: (a)the domain (b)f(1) (c)f(2) (d)f(3) (e)f(0.1)

The Parkers are borrowing $120,000 to buy a house.Their monthly payment amount is given by where r is the monthly interest rate and n is the number of months.What is the Parker's monthly payment if they get: (a)a 30-year loan at 9% annual interest? (b)a 20-year loan at 10% annual interest?

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

Use a graphing calculator to find the maximum value of f(x)and the minimum value of f(x)for the indicated values of x: ;

If f(x)= - - 2x - 6,then f(2)- f(t)=

The proceeds from an event depend on the number of people who attend. (a)Write a function p(n)for the proceeds if each ticket costs $8.00 and the number of tickets sold is n. (b)What is the domain of this function out of context? (c)What is the domain of this function in the given context? (d)Find p(c),p(c + 5),and p(c + 25). (e)What happens to the proceeds when the number who attend increases by a constant m? Describe using an equation.

Sketch a graph of f(x)= - 3

Determine the x- and y-intercepts,if they exist,of the graph of 9 + + 8y = 9.Also determine whether the graph is symmetric about the x-axis,the y-axis,the origin,or the line y = x.

Find the domain: