Exam 2: Functions and Graphs

Since life expectancy has increased in the last century, the number of Alzheimer's patients has increased dramatically. The number of patients in the United States reached 4 million in 2000. Using data collected since 2000, it has been found that the data can be modeled by the exponential function where x is the years since 2000. Estimate the Alzheimer's patients in 2025. Round to the nearest tenth.

Determine if the equation specifies a function with independent variable x. If so, find the domain. If not, find a value of x to which there corresponds more than one value of y: -xy = -5 A) A function with domain all real numbers except x = 0 B) Not a function; for example, when x = -5, y = ±1

Find the vertex and the maximum or minimum of the quadratic function by first writing f in standard form. State the range of f and find the intercepts of f .

Graph the function. -

Determine if the equation specifies a function with independent variable x. If so, find the domain. If not, find a value of x to which there corresponds more than one value of y: -x² + y² = 36 A) A function with domain ℛ B) Not a function; for example, when x = 0, y = ±6

If $4,000 is invested at 7% compounded annually, how long will it take for it to grow to $6,000, assuming no withdrawals are made? Compute answer to the next higher year if not exact.

For the rational function below (i) Find the intercepts for the graph; (ii) Determine the domain; (iii) Find any vertical or horizontal asymptotes for the graph; (iv) Sketch any asymptotes as dashed lines. Then sketch the graph of y = f(x). -

In economics, functions that involve revenue, cost and profit are used. Suppose R(x) and C(x) denote the total revenue and the total cost, respectively, of producing a new high-tech widget. The difference represents the total profit for producing x widgets. Given R(x) = 60x - 0.4 and find the equation for P(x).

Use the properties of logarithms to solve: -

Determine whether there is a maximum or minimum value for the given function, and find that value: -

Solve the equation graphically to four decimal places: -

Find the function value: -

Solve for x to two decimal places (using a calculator): -

Convert to a logarithmic equation. -

Use a calculator to evaluate the expression. Round the result to five decimal places: -ln 1097

Find the function value: -Given that , find f(t + 2).

A professional basketball player has a vertical leap of 37 inches. A formula relating an athlete's vertical leap V, in inches, to hang time T, in seconds, is V= . What is his hang time? Round to the nearest tenth.

Use a calculator to evaluate the expression. Round the result to five decimal places: -ln 0.027

The number of reports of a certain virus has increased exponentially since 1960. The current number of cases can be approximated using the function where t is the number of years since 1960. Estimate the of cases in the year 2010.

Find the vertex form for the quadratic function. Then find each of the following: (A) Intercepts (B) Vertex (C) Maximum or minimum (D) Range -