Solved: Trees grow faster and form wider rings in warm years and grow more slowly and

If f sxd x 1 s2 2 x and tsud u 1 s2 2 u , is it true that f t?

If fsxd x 2 2 x x 2 1 and tsxd x is it true that f t?

The graph of a function f is given. (a) State the value of fs1d. (b) Estimate the value of fs21d. (c) For what values of x is fsxd 1? (d) Estimate the value of x such that fsxd 0. (e) State the domain and range of f. (f) On what interval is f increasing?

The graphs of f and t are given. g x y 0 f 2 2 (a) State the values of fs24d and ts3d. (b) For what values of x is fsxd tsxd? (c) Estimate the solution of the equation fsxd 21. (d) On what interval is f decreasing? (e) State the domain and range of f. (f) State the domain and range of t.

Figure 1 was recorded by an instrument operated by the California Department of Mines and Geology at the University Hospital of the University of Southern California in Los Angeles. Use it to estimate the range of the vertical ground acceleration function at USC during the Northridge earthquake

In this section we discussed examples of ordinary, everyday functions: Population is a function of time, postage cost is a function of weight, water temperature is a function of time. Give three other examples of functions from everyday life that are described verbally. What can you say about the domain and range of each of your functions? If possible, sketch a rough graph of each function.

Determine whether the curve is the graph of a function of x. If it is, state the domain and range of the function

Determine whether the curve is the graph of a function of x. If it is, state the domain and range of the function

Determine whether the curve is the graph of a function of x. If it is, state the domain and range of the function

Determine whether the curve is the graph of a function of x. If it is, state the domain and range of the function

Shown is a graph of the global average temperature T during the 20th century. Estimate the following. (a) The global average temperature in 1950 (b) The year when the average temperature was 14.2C (c) The year when the temperature was smallest? Largest? (d) The range of T

Trees grow faster and form wider rings in warm years and grow more slowly and form narrower rings in cooler years. The figure shows ring widths of a Siberian pine from 1500 to 2000. (a) What is the range of the ring width function? (b) What does the graph tend to say about the temperature of the earth? Does the graph reflect the volcanic eruptions of the mid-19th century?

You put some ice cubes in a glass, fill the glass with cold water, and then let the glass sit on a table. Describe how the temperature of the water changes as time passes. Then sketch a rough graph of the temperature of the water as a function of the elapsed time.

Three runners compete in a 100-meter race. The graph depicts the distance run as a function of time for each runner. Describe in words what the graph tells you about this race. Who won the race? Did each runner finish the race?

The graph shows the power consumption for a day in September in San Francisco. (P is measured in megawatts; t is measured in hours starting at midnight.) (a) What was the power consumption at 6 am? At 6 pm? (b) When was the power consumption the lowest? When was it the highest? Do these times seem reasonable?

Sketch a rough graph of the number of hours of daylight as a function of the time of year.

Sketch a rough graph of the outdoor temperature as a function of time during a typical spring day.

Sketch a rough graph of the market value of a new car as a function of time for a period of 20 years. Assume the car is well maintained.

Sketch the graph of the amount of a particular brand of coffee sold by a store as a function of the price of the coffee.

You place a frozen pie in an oven and bake it for an hour. Then you take it out and let it cool before eating it. Describe how the temperature of the pie changes as time passes. Then sketch a rough graph of the temperature of the pie as a function of time

A homeowner mows the lawn every Wednesday afternoon. Sketch a rough graph of the height of the grass as a function of time over the course of a four-week period.

An airplane takes off from an airport and lands an hour later at another airport, 400 miles away. If t represents the time in minutes since the plane has left the terminal building, let xstd be the horizontal distance traveled and ystd be the altitude of the plane. (a) Sketch a possible graph of xstd. (b) Sketch a possible graph of ystd. (c) Sketch a possible graph of the ground speed. (d) Sketch a possible graph of the vertical velocity.

Temperature readings T (in F) were recorded every two hours from midnight to 2:00 pm in Atlanta on June 4, 2013. The time t was measured in hours from midnight. t 0 2 4 6 8 10 12 14 T 74 69 68 66 70 78 82 86 (a) Use the readings to sketch a rough graph of T as a function of t. (b) Use your graph to estimate the temperature at 9:00 am.

Researchers measured the blood alcohol concentration (BAC) of eight adult male subjects after rapid consumption of 30 mL of ethanol (corresponding to two standard alcoholic drinks). The table shows the data they obtained by averaging the BAC (in mgymL) of the eight men. (a) Use the readings to sketch the graph of the BAC as a function of t. (b) Use your graph to describe how the effect of alcohol varies with time.

If fsxd 3x 2 2 x 1 2, find fs2d, fs22d, fsad, fs2ad, fsa 1 1d, 2fsad, fs2ad, fsa2 d, [ fsad] 2 , and fsa 1 hd.

A spherical balloon with radius r inches has volume Vsrd 4 3r 3 . Find a function that represents the amount of air required to inflate the balloon from a radius of r inches to a radius of r 1 1 inches.

Evaluate the difference quotient for the given function. Simplify your answer. fsxd 4 1 3x 2 x 2 , fs3 1 hd 2 fs3d h

Evaluate the difference quotient for the given function. Simplify your answer. fsxd x 3 , fsa 1 hd 2 fsad h

Evaluate the difference quotient for the given function. Simplify your answer. fsxd 1 x , fsxd 2 fsad x 2 a

Evaluate the difference quotient for the given function. Simplify your answer. fsxd x 1 3 x 1 1 , fsxd 2 fs1d x 2 1

Find the domain of the function. fsxd x 1 4 x 2 2 9

Find the domain of the function. fsxd 2x 3 2 5 x 2 1 x 2 6

Find the domain of the function. fstd s 3 2t 2 1

Find the domain of the function. tstd s3 2 t 2 s2 1 t

Find the domain of the function. hsxd 1 s 4 x 2 2 5x

Find the domain of the function.fsud u 1 1 1 1 1 u 1 1

Find the domain of the function. Fspd s2 2 sp

Find the domain and range and sketch the graph of the function hsxd s4 2 x 2 .

Find the domain and sketch the graph of the function. fsxd 1.6x 2 2.4

Find the domain and sketch the graph of the function. tstd t 2 2 1 t 1 1

Evaluate fs23d, fs0d, and fs2d for the piecewise defined function. Then sketch the graph of the function. fsxd H x 1 2 1 2 x if x , 0 if x > 0

Evaluate fs23d, fs0d, and fs2d for the piecewise defined function. Then sketch the graph of the function.fsxd H 3 2 1 2 x 2x 2 5 if x , 2 if x > 2

Evaluate fs23d, fs0d, and fs2d for the piecewise defined function. Then sketch the graph of the function. f sxd H x 1 1 x 2 if x < 21 if x . 21

Evaluate fs23d, fs0d, and fs2d for the piecewise defined function. Then sketch the graph of the function. f sxd H 21 7 2 2x if x < 1 if x . 1

Sketch the graph of the function fsxd x 1 | x

Sketch the graph of the function fsxd | x 1 2 |

Sketch the graph of the functiont std |1 2 3t |

Sketch the graph of the function hstd | t | 1 | t 1 1

Sketch the graph of the function f sxd H| x | 1 if | x | < 1 if | x | . 1

Sketch the graph of the function sxd || x | 2 1|

Find an expression for the function whose graph is the given curve. The line segment joining the points s1, 23d and s5, 7d

Find an expression for the function whose graph is the given curve. The line segment joining the points s25, 10d and s7, 210d

Find an expression for the function whose graph is the given curve. The bottom half of the parabola x 1 s y 2 1d 2 0

Find an expression for the function whose graph is the given curve. The top half of the circle x 2 1 s y 2 2d 2 4

Find an expression for the function whose graph is the given curve.

Find an expression for the function whose graph is the given curve.

Find a formula for the described function and state its domain. A rectangle has perimeter 20 m. Express the area of the rectangle as a function of the length of one of its sides.

Find a formula for the described function and state its domain. A rectangle has area 16 m2 . Express the perimeter of the rectangle as a function of the length of one of its sides.

Find a formula for the described function and state its domain. Express the area of an equilateral triangle as a function of the length of a side.

Find a formula for the described function and state its domain. A closed rectangular box with volume 8 ft3 has length twice the width. Express the height of the box as a function of the width.

An open rectangular box with volume 2 m3 has a square base. Express the surface area of the box as a function of the Find a formula for the described function and state its domain.length of a side of the base.

A Norman window has the shape of a rectangle surmounted by a semicircle. If the perimeter of the window is 30 ft, express the area A of the window as a function of the width x of the window.

A box with an open top is to be constructed from a rectangular piece of cardboard with dimensions 12 in. by 20 in. by cutting out equal squares of side x at each corner and then folding up the sides as in the figure. Express the volume V of the box as a function of x.

A cell phone plan has a basic charge of $35 a month. The plan includes 400 free minutes and charges 10 cents for each additional minute of usage. Write the monthly cost C as a function of the number x of minutes used and graph C as a function of x for 0 < x < 600.

In a certain state the maximum speed permitted on freeways is 65 miyh and the minimum speed is 40 miyh. The fine for violating these limits is $15 for every mile per hour above the maximum speed or below the minimum speed. Express the amount of the fine F as a function of the driving speed x and graph Fsxd for 0 < x < 100.

An electricity company charges its customers a base rate of $10 a month, plus 6 cents per kilowatt-hour (kWh) for the first 1200 kWh and 7 cents per kWh for all usage over 1200 kWh. Express the monthly cost E as a function of the amount x of electricity used. Then graph the function E for 0 < x < 2000.

In a certain country, income tax is assessed as follows. There is no tax on income up to $10,000. Any income over $10,000 is taxed at a rate of 10%, up to an income of $20,000. Any income over $20,000 is taxed at 15%. (a) Sketch the graph of the tax rate R as a function of the income I. (b) How much tax is assessed on an income of $14,000? On $26,000? (c) Sketch the graph of the total assessed tax T as a function of the income I.

The functions in Example 10 and Exercise 67 are called step functions because their graphs look like stairs. Give two other examples of step functions that arise in everyday life.

Graphs of f and t are shown. Decide whether each function is even, odd, or neither. Explain your reasoning.

Graphs of f and t are shown. Decide whether each function is even, odd, or neither. Explain your reasoning.

(a) If the point s5, 3d is on the graph of an even function, what other point must also be on the graph? (b) If the point s5, 3d is on the graph of an odd function, what other point must also be on the graph?

A function f has domain f25, 5g and a portion of its graph is shown. (a) Complete the graph of f if it is known that f is even. (b) Complete the graph of f if it is known that f is odd.

Determine whether f is even, odd, or neither. If you have a graphing calculator, use it to check your answer visually. fsxd x x 2 1 1

Determine whether f is even, odd, or neither. If you have a graphing calculator, use it to check your answer visually. fsxd x 2 x 4 1 1

Determine whether f is even, odd, or neither. If you have a graphing calculator, use it to check your answer visually. fsxd x x 1 1

Determine whether f is even, odd, or neither. If you have a graphing calculator, use it to check your answer visually. fsxd x | x |

Determine whether f is even, odd, or neither. If you have a graphing calculator, use it to check your answer visually. fsxd 1 1 3x 2 2 x 4

Determine whether f is even, odd, or neither. If you have a graphing calculator, use it to check your answer visually. fsxd 1 1 3x 3 2 x 5

If f and t are both even functions, is f 1 t even? If f and t are both odd functions, is f 1 t odd? What if f is even and t is odd? Justify your answers.

If f and t are both even functions, is the product ft even? If f and t are both odd functions, is ft odd? What if f is even and t is odd? Justify your answers.