Exam 2: Functions, Limits and the Derivative

Use the vertical-line test to determine whether the graph represents y as a function of x. Answer yes or no.

Find the indicated one-sided limit.

Determine whether the given function is a polynomial function or rational function. State the degree, if it is a polynomial function.

Use the graph of the function f to find and if the limit exists.

Evaluate h (3), where

Determine whether the given function is a polynomial function or rational function. State the degree, if it is a polynomial function. Answer polynomial or rational. __________ If a polynomial function, the degree is __________

Economists define the disposable annual income for an individual by the equation D = (1 - r)T, where T is the individual's total income and r is the net rate at which he or she is taxed. What is the disposable income for an individual whose income is $80,000 and whose net tax rate is 21%? $__________

Determine whether the equation defines y as a linear function of x. Answer yes or no.

Let and . Find the rule for the function

A study prepared for a Sunbelt town's Chamber of Commerce projected that the population of the town in the next 5 yr will grow according to the rule where P(x) denotes the population x mo from now. By how much will the population increase during the next 4 mo? __________ During the next 16 mo? __________

The volume of a spherical cancerous tumor is given by the function where r is the radius of the tumor in centimeters. By what factor is the volume of the tumor increased if its radius is decuple?

Find of the functions.

Let , . Find the rule for the function

Find function f such that and

An apple orchard has an average yield of 37 bushels of apples/tree if tree density is 22 trees/acre. For each unit increase in tree density, the yield decreases by 3 bushels. Letting x denote the number of trees beyond 22/acre, find a function in x that gives the yield of apples.

Find the indicated limit, if it exists.

Use the four-step process to find the slope of the tangent line to the graph of the given function at any point. __________

Find and , where

Find the one-sided limit.

Find the limit, if it exists.