Life expectancy improved dramatically in the 20th century.

Let f be the function whose graph is given

The graph of t is given.

If fsxd x 2 2 2x 1 3, evaluate the difference quotient fsa 1 hd 2 fsad h

Sketch a rough graph of the yield of a crop as a function of the amount of fertilizer used.

Find the domain and range of the function. Write your answer in interval notation.

Find the domain and range of the function. Write your answer in interval notation.

Find the domain and range of the function. Write your answer in interval notation.

Find the domain and range of the function. Write your answer in interval notation.

Suppose that the graph of f is given. Describe how the graphs of the following functions can be obtained from the graph of f. (a) y fsxd 1 8 (b) y fsx 1 8d (c) y 1 1 2fsxd (d) y fsx 2 2d 2 2 (e) y 2fsxd (f) y f 21 sxd

The graph of f is given. Draw the graphs of the following functions. (a) y fsx 2 8d (b) y 2fsxd (c) y 2 2 fsxd (d) y 1 2 fsxd 2 1 (e) y f 21 sxd (f) y f 21 sx 1 3d

Use transformations to sketch the graph of the function

Use transformations to sketch the graph of the function

Use transformations to sketch the graph of the function

Use transformations to sketch the graph of the function

Use transformations to sketch the graph of the function

Use transformations to sketch the graph of the function

Determine whether f is even, odd, or neither even nor odd. (a) fsxd 2x 5 2 3x 2 1 2 (b) fsxd x 3 2 x 7 (c) fsxd e 2x 2 (d) fsxd 1 1 sin x

Find an expression for the function whose graph consists of the line segment from the point s22, 2d to the point s21, 0d together with the top half of the circle with center the origin and radius 1.

If fsxd ln x and tsxd x 2 2 9, ind the functions (a) f 8 t, (b) t 8 f, (c) f 8 f, (d) t 8 t, and their domains

Express the function Fsxd 1ysx 1 sx as a composition of three functions.

Life expectancy improved dramatically in the 20th century. The table gives the life expectancy at birth (in years) of males born in the United States. Use a scatter plot to choose an appropriate type of model. Use your model to predict the life span of a male born in the year 2010

A small-appliance manufacturer inds that it costs $9000 to produce 1000 toaster ovens a week and $12,000 to produce 1500 toaster ovens a week. (a) Express the cost as a function of the number of toaster ovens produced, assuming that it is linear. Then sketch the graph. (b) What is the slope of the graph and what does it represent? (c) What is the y-intercept of the graph and what does it represent?

If fsxd 2x 1 ln x, ind f 21 s2d

Find the inverse function of fsxd x 1 1 2x 1 1 .

Find the exact value of each expression. (a) e 2 ln 3 (b) log10 25 1 log10 4 (c) tansarcsin 1 2 d (d) sinscos21 s 4 5 dd

Solve each equation for x. (a) e x 5 (b) ln x 2 (c) e e x 2 (d) tan21 x 1

The half-life of palladium-100, 100Pd, is four days. (So half of any given quantity of 100Pd will disintegrate in four days.) The initial mass of a sample is one gram. (a) Find the mass that remains after 16 days. (b) Find the mass mstd that remains after t days. (c) Find the inverse of this function and explain its meaning. (d) When will the mass be reduced to 0.01g?

The population of a certain species in a limited environment with initial population 100 and carrying capacity 1000 is Pstd 100,000 100 1 900e 2t where t is measured in years. (a) Graph this function and estimate how long it takes for the population to reach 900. (b) Find the inverse of this function and explain its meaning. (c) Use the inverse function to ind the time required for the population to reach 900. Compare with the result of part (a)