If f (x) – 3x2 – x + 2, and f (2), f (-2), f (a), f (-a), f (a+1), 2 f (a), f (2a), f (a2), [f (a)]2, and f (a + h).
> How many significant figures are represented in each of the following numbers? a. 3.8 × 10-3 b. 5.20 × 102 c. 0.00261 d. 24 e. 240 f. 2.40
> Explain what is meant by each of the following terms: a. error b. uncertainty
> Determine the temperature reading of the following thermometer to the correct number of significant figures. | 25.2 | 25.3
> Rank the following from least to greatest mass. cg, µg, Mg
> What English unit of volume is similar to a L?
> What metric unit for length is similar to the English yd?
> Explain the difference between mass and weight.
> Classify the matter represented in the following diagram by state and by composition. DO000000000 DO0000000000 = atom
> Label each property as intensive or extensive: a. the shape of leaves on a tree b. the number of leaves on a tree
> Label each of the following as either a homogeneous mixture or a heterogeneous mixture: a. gasoline b. vegetable soup c. concrete d. hot coffee
> Label each of the following as either a pure substance or a mixture: a. sucrose (table sugar) b. orange juice c. urine d. tears
> Label each of the following properties of sodium as either a physical property or a chemical property: a. When exposed to air, sodium forms a white oxide. b. The density of sodium metal at 250C is 0.97 g/cm3.
> Label each of the following as either a physical change or a chemical reaction: a. A puddle of water evaporates. b. Food is digested. c. Wood is burned.
> Draw a diagram representing a homogeneous mixture of two different substances. Use two different colored spheres to represent the two different substances.
> Label each of the following as pertaining to either a solid, liquid, or gas. a. It has a fixed volume, but not a fixed shape. b. The attractive forces between particles are very pronounced. c. The particles are far apart.
> List the differences between chemical changes and physical changes.
> Distinguish between an intensive property and an extensive property.
> Describe what is meant by an extensive property and give an example.
> Give examples of pure substances and mixtures.
> Classify each of the following as either a chemical property or a physical property: a. odor b. taste c. temperature
> Explain the differences among the three states of matter in terms of volume and shape.
> Describe an experiment that would enable you to determine the mass (g) of solids suspended in a 1-L sample of seawater.
> Observed increases in global temperatures are caused by elevated levels of carbon dioxide. Is this statement a theory or a scientific law? Explain your reasoning.
> Describe an application of reasoning involving the scientific method that has occurred in your day-to-day life.
> Discuss the difference between theory and scientific law.
> The model of methane in Question 1.27 has limitations, as do all models. What are these limitations? Question 1.27: What are the characteristics of methane emphasized by the following model? H H°c H H
> What data would be required to estimate the mass of planet earth?
> Why is observation a critical starting point for any scientific study?
> Define energy and explain the importance of energy in chemistry.
> Convert 2.00 × 102 J to units of cal.
> Cloudy urine can be a symptom of a bladder infection. Classify this urine as a pure substance, a homogeneous mixture, or a heterogeneous mixture.
> Find the domain and sketch the graph of the function. f (x) = {(x+2 & if & x < -1 @ x2 & if & x > -1)
> Find the domain and sketch the graph of the function. f (x) = {(x+2 & if & x
> Find the domain and sketch the graph of the function. g (x) = |x | - x
> Find the domain and sketch the graph of the function. G (x) = |3x +|x|/x
> Find the domain and sketch the graph of the function. F (x) = |2x + 1|
> Find the domain and sketch the graph of the function. g (x) = √x - 5
> Find the domain and sketch the graph of the function. H (t) = 4 - t2/ 2 - t
> Evaluate the difference quotient for the given function. Simplify your answer. f(x) – x², fla + h) – f(a)
> Find the domain and sketch the graph of the function. F (x) = x2 - 2x + 1
> Find an expression for a cubic function f if f (1) and f (-1) = f (0) = f (2) = 0.
> Find the domain and range and sketch the graph of the function h (x) = √4 – x2.
> Evaluate the difference quotient for the given function. Simplify your answer. f(3 + h) – f(3) f(x) – 4 + 3x – x², h
> Find the domain of the function. g (t) = √3 - t - √2 + t
> Find the domain of the function. f (t) = 3√2t - 1
> Find the domain of the function. f (x) = 2x3 – 5/x2 + x - 6
> Find the domain of the function. f (x) = x + 4/x2 - 9
> Evaluate the difference quotient for the given function. Simplify your answer. f(x) – f(a) f(x) – х — а
> A spherical balloon with radius r inches has volume V(r)-4/3πr3. 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 inches.
> Temperature readings T (in °F) were recorded every two hours from midnight to 2:00 PM in Baltimore on September 26, 2007. The time was measured in hours from midnight. (a). Use the readings to sketch a rough graph of T as a function of t. (b
> (a). How is the graph of y = 2 sin x related to the graph of y = sin x? Use your answer and Figure 6 to sketch the graph of y = 2 sin x. (b). How is the graph of y = 1 + √x related to the graph of y = √x? Use your answer and Figure 4(a) to sketch the gra
> The number N (in millions) of US cellular phone subscribers is shown in the table. (Midyear estimates are given.) (a). Use the data to sketch a rough graph of N as a function of (b). Use your graph to estimate the number of cell-phone subscribers at mi
> 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 x(t) be the horizontal distance traveled and y (t) be the altitude o
> 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.
> 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 tim
> 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.
> If and are both even functions, is the product fg even? If f and g are both odd functions, is fg odd? What if f is even and g is odd? Justify your answers.
> If and are both even functions, is f + g even? If and are both odd functions, is f + g odd? What if f is even and g is odd? Justify your answers.
> Determine whether f is even, odd, or neither. If you have a graphing calculator, use it to check your answer visually. f(x) = 1 + 3x – x³
> The graph shown gives the weight of a certain person as a function of age. Describe in words how this person’s weight varies over time. What do you think happened when this person was 30 years old? 200 150 weight (рounds) 100f 50t
> Find the domain and sketch the graph of the function. f (t) = 2t + t2
> The graphs of f and t are given. (a). State the values of f (-4) and g (3). (b). For what values of is f (x) – g (x)? (c). Estimate the solution of the equation f (x) = -1. (d). On what interval is f decreasing? (e). State the domain
> Find the functions (a) f0g, (b) g0f, (c) f0f, and (d)g0g and their domains. x + 1 f(x) = x + g(x) = x + 2
> 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 des
> Graphs of f and g are shown. Decide whether each function is even, odd, or neither. Explain your reasoning.
> A function f has domain [-5, 5] 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. y. -5 5
> (a). If the point (5, 3) is on the graph of an even function, what other point must also be on the graph? (b). If the point (5, 3) is on the graph of an odd function, what other point must also be on the graph?
> Suppose t is an odd function and let h = f 0 g. Is h always an odd function? What if f is odd? What if f is even?
> 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 rat
> The functions in Example 10 and Exercise 61(a) are called step functions because their graphs look like stairs. Give two other examples of step functions that arise in everyday life. Exercise 61(a): (a). Sketch the graph of the tax rate R as a function
> (a). If and g (x) = 2x + 1, find h (x) = 4x2 + 4x + 7 find a function f such that f 0 g. (Think about what operations you would have to perform on the formula for to end up with the formula for g.) (b). If f (x) = 2x + 1 and h (x) = 3x2 + 3x + 2, find a
> Match each equation with its graph. Explain your choices. (Don’t use a computer or graphing calculator.) y (а) у — х? (b) y = x (c) y = x*
> The graph of a function is given. (a). State the value of f. (b). Estimate the value of f. (c). For what values of is f (x) – 1? (d). Estimate the value of such that f. (e). State the domain and range of f. (f). On what interval is in
> 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 at each corner and then folding up the sides as in the figure. Express the volume V of the box as a fu
> Classify each function as a power function, root function, polynomial (state its degree), rational function, algebraic function, trigonometric function, exponential function, or logarithmic function. (a) y = 7* (b) y = x" (c) у — х*(2 — х') (d) y =
> The Heaviside function H is defined by It is used in the study of electric circuits to represent the sudden surge of electric current, or voltage, when a switch is instantaneously turned on. (a). Sketch the graph of the Heaviside function. (b). Sketch
> Find an expression for the function whose graph is the given curve. 1
> A ship is moving at a speed of 30 km/h parallel to a straight shoreline. The ship is 6 km from shore and it passes a lighthouse at noon. (a). Express the distance between the lighthouse and the ship as a function of d, the distance the ship has traveled
> 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. A rectangle has perimeter 20 m. Express the area of the rectangle as a function of the length of one of its sides.
> Find an expression for the function whose graph is the given curve. y
> Use the given graphs of f and g to evaluate each expression, or explain why it is undefined. g 2. 2 (a) f(g(2)) (d) (gof)(6) (b) g(f(0)) (e) (g ° g)(-2) (c) (f° g)(0) (f) (f°f)(4)
> Classify each function as a power function, root function, polynomial (state its degree), rational function, algebraic function, trigonometric function, exponential function, or logarithmic function. (a) f(x) = log2x (b) g(x) = V %3D 2x (c) h(x) = (
> The graph of f is given. Use it to graph the following functions. (a). y = f (2x) (b). y = f (1/2x) (c). y = f (-x) (d). y = -f (-x) 1. 1
> Find an expression for the function whose graph is the given curve. The bottom half of the parabola x + (y -1)2 = 0
> The graph shows the power consumption for a day in September in San Francisco. (P is measured in megawatts; 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
> The city of New Orleans is located at latitude 300N. Use Figure 9 to find a function that models the number of hours of daylight at New Orleans as a function of the time of year. To check the accuracy of your model, use the fact that on March 31 the sun
> The table gives the winning heights for the Olympic pole vault competitions up to the year 2000. (a). Make a scatter plot and decide whether a linear model is appropriate. (b). Find and graph the regression line. (c). Use the linear model to predict th
> Biologists have observed that the chirping rate of crickets of a certain species appears to be related to temperature. The table shows the chirping rates for various temperatures. (a). Make a scatter plot of the data. (b). Find and graph the regression
> Find the domain and sketch the graph of the function. f (x) = {(3 -1/2x & if & x > 0 @ 2x -5 & if & x > 0)
> The table shows (lifetime) peptic ulcer rates (per 100 population) for various family incomes as reported by the National Health Interview Survey. (a). Make a scatter plot of these data and decide whether a linear model is appropriate. (b). Find and gr
> Biologists have noticed that the chirping rate of crickets of a certain species is related to temperature, and the relationship appears to be very nearly linear. A cricket produces 113 chirps per minute at and 173 0F chirps per minute at 800F. (a). Find
> The relationship between the Fahrenheit (F) and Celsius (C) temperature scales is given by the linear function F = 9/5C +32. (a). Sketch a graph of this function. (b). What is the slope of the graph and what does it represent? What is the F-intercept and
> 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 functio
> The graph of is given. Draw the graphs of the following functions. (a). y = f (x) -2 (b). y = f (x -2) (c). y = -2 f(x) (d). y = f (1/3x) + 1 2 1
> 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? у (m) A B C 100 20 t
> The first graph in the figure is that of y = sin 45 x as displayed by a TI-83 graphing calculator. It is inaccurate and so, to help explain its appearance, we replot the curve in dot mode in the second graph. What two sine curves does the calculator appe
> The figure shows the graphs of y = sin 96 x and y = sin 2x as displayed by a TI-83 graphing calculator. The first graph is inaccurate. Explain why the two graphs appear identical. [Hint: The TI-83’s graphing window is 95 pixels wide. Wh
> Find expressions for the quadratic functions whose graphs are shown. (-2, 2), (0, 1) (4, 2) 3 4(1, –2.5)
> What happens to the graph of the equation y2 = cx3 + x2 as c varies?
