Question: Determine an appropriate viewing rectangle for the

> Let and be linear functions with equations f (x) = mx + b1 and g (x) m2x + b2. Is f 0 g also a linear function? If so, what is the slope of its graph?

> The Heaviside function defined in Exercise 57 can also be used to define the ramp function y = ct H (t), which represents a gradual increase in voltage or current in a circuit. Exercise 57: The Heaviside function H is defined by It is used in the stu

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

> An airplane is flying at a speed of at an altitude of 350 mi/h one mile and passes directly over a radar station at time t = 0. (a). Express the horizontal distance (in miles) that the plane has flown as a function of t. (b). Express the distance between

> 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.

> A spherical balloon is being inflated and the radius of the balloon is increasing at a rate of 2 cm/s. (a). Express the radius of the balloon as a function of the time t (in seconds). (b). If V is the volume of the balloon as a function of the radius, fi

> A stone is dropped into a lake, creating a circular ripple that travels outward at a speed of 60 m/s. (a). Express the radius of this circle as a function of the time (in seconds). (b). If A is the area of this circle as a function of the radius, find A

> Use the given graphs of f and g to estimate the value of f (g (x)) for x = -5, -4, -3…5. Use these estimates to sketch a rough graph of f 0 g. 지

> Recent studies indicate that the average surface temperature of the earth has been rising steadily. Some scientists have modeled the temperature by the linear function T = 0.002t + 8.50, where T is temperature in 0Cand represents years since 1900. (a). W

> The monthly cost of driving a car depends on the number of miles driven. Lynn found that in May it cost her $380 to drive 480 mi and in June it cost her $460 to drive 800 mi. (a). Express the monthly cost C as a function of the distance driven d assuming

> Use the table to evaluate each expression. 3 4 1 5 6. f(x) 3 4 5 9(x) 6 1 3. 2. 2. 2. 2. 2. 3. (a) f(g(1)) (d) g(g(1)) (b) g(f(1)) (e) (gof)(3) (c) f(f(1)) (f) (fo g)(6)

> Express the function in the form f o g 0 h. H (x) = sec4 (√x)

> Express the function in the form f o g 0 h. H (x) = 8√2 + |x|

> Express the function in the form f o g 0 h. H (x) = 1 - 3x2

> Express the function in the form fog. u (t) = tan 6/1 + tan t

> Express the function in the form f0g. u (t) = √cos t

> Express the function in the form f0g. G (x) = 3√x/1+x

> Express the function in the form f0g. F (x) = 3√x/1 + 3√x

> Express the function in the form f0g. F (x) = cos2x

> Express the function in the form f0g. F (x) = (2x + x2)4

> At the surface of the ocean, the water pressure is the same as the air pressure above the water, 15 lb/in2. Below the surface, the water pressure increases by 4.34 lb/in2 for every 10 ft of descent. (a). Express the water pressure as a function of the de

> Find f0g0h. f (x) = tan x, g (x) = x/x-1, h (x) = 3√x

> Find f0g0h. f (x) = √x - 3 g (x) = x2 h (x) = x3 + 2

> Find f0g0h. f (x) = 2x - 1 g (x) = x2 h (x) = 1 - x

> Find f0g0h. f (x) = x + 1 g(x) = 2x h (x) = x - 1

> This exercise explores the effect of the inner function on a composite function y = f (g (x)). (a). Graph the function y = sin (√x) using the viewing rectangle [0, 400] by [-1.5, 1.5]. How does this graph differ from the graph of the sine function? (b).

> Find the domain and sketch the graph of the function. f (x) = 2 - 0.4x

> The curves with equations y = |x| / √c – x2 are called bullet-nose curves. Graph some of these curves to see why. What happens as c increases?

> Graph the function y = xn2-x, x > 0, for n = 1, 2 ,3, 4, 5 and 6. How does the graph change as n increases?

> Find the functions (a) f0g, (b) g0f, (c) f0f, and (d)g0g and their domains. f(x) — х — 2, д() — х* + Зх + 4

> Find the functions (a) f0g, (b) g0f, (c) f0f, and (d)g0g and their domains. f(x) = x ? - 1, g(x) = 2x + 1

> The manager of a furniture factory finds that it costs $2200 to manufacture 100 chairs in one day and $4800 to produce 300 chairs in one day. (a). Express the cost as a function of the number of chairs produced, assuming that it is linear. Then sketch th

> Find (a) f + g, (b) f - g, (c) fg, and (d) f/g and state their domains. f(x) = /3 – x, g(x) = /x² – 1

> Find (a) f + g, (b) f - g, (c) fg, and (d) f/g and state their domains. f(x) = x³ + 2x?, g(x) = 3x² – 1

> Graph the polynomials P (x) = 3x2 – 5x3 + 2x and Q (x) = 3x5 on the same screen, first using the viewing rectangle [-2, 2] by [-2, 2] and then changing to [-10, 10] by [-10000, 10000]. What do you observe from these graphs?

> (a). How is the graph of y = f (|x|) related to the graph of f? (b). Sketch the graph of y = sin |x|. (c). Sketch the graph of y = √|x|

> Use graphs to determine which of the functions f (x) = x4 - 100x3 and g (x) = x3 is eventually larger.

> Use the data in the table to model the population of the world in the 20th century by a cubic function. Then use your model to estimate the population in the year 1925. Population (millions) Population (millions) Year Year 1900 1650 1960 3040 1910 1

> We saw in Example 9 that the equation cos x = x has exactly one solution. (a) Use a graph to show that the equation cos x = 0.3 x has three solutions and find their values correct to two decimal places. (b) Find an approximate value of m such that the eq

> Graph the function by hand, not by plotting points, but by starting with the graph of one of the standard functions given in Section 1.2, and then applying the appropriate transformations. y

> Graph the function by hand, not by plotting points, but by starting with the graph of one of the standard functions given in Section 1.2, and then applying the appropriate transformations. tan 4 x 4

> Graph the function by hand, not by plotting points, but by starting with the graph of one of the standard functions given in Section 1.2, and then applying the appropriate transformations. y = |x – 2|

> (a). Try to find an appropriate viewing rectangle for f (x) = (x – 10)3 2-x. (b). Do you need more than one window? Why?

> Do the graphs intersect in the given viewing rectangle? If they do, how many points of intersection are there? у — 6 — 4х — х, у — Зr + 18; [-6, 2] by [-5, 20]

> Do the graphs intersect in the given viewing rectangle? If they do, how many points of intersection are there? у — Зx? — бх + 1, у-0.23х — 2.25; [-1, 3] by [-2.5, 1.5]

> Graph the hyperbola by graphing the functions y2 – 9x2 = 1 whose graphs are the upper and lower branches of the hyperbola.

> Graph the ellipse by graphing the functions 4x2 + 2y2 = 1 whose graphs are the upper and lower halves of the ellipse.

> Graph the function f (x) = x2 √30 – x in an appropriate viewing rectangle. Why does part of the graph appear to be missing?

> Graph the function by hand, not by plotting points, but by starting with the graph of one of the standard functions given in Section 1.2, and then applying the appropriate transformations. y = sin (x/2)

> Graph the function by hand, not by plotting points, but by starting with the graph of one of the standard functions given in Section 1.2, and then applying the appropriate transformations. y = 1 + 2 cos x

> Determine an appropriate viewing rectangle for the given function and use it to draw the graph. f(x) = sec(207x)

> Graph the function by hand, not by plotting points, but by starting with the graph of one of the standard functions given in Section 1.2, and then applying the appropriate transformations. y = (x + 1)2

> Jason leaves Detroit at 2:00 PM and drives at a constant speed west along I-96. He passes Ann Arbor, 40 mi from Detroit, at 2:50 PM. (a). Express the distance traveled in terms of the time elapsed. (b). Draw the graph of the equation in part (a). (c). Wh

> Determine an appropriate viewing rectangle for the given function and use it to draw the graph. f() — сos(0.001x)

> Determine an appropriate viewing rectangle for the given function and use it to draw the graph. f(x) = sin (1000x)

> Determine an appropriate viewing rectangle for the given function and use it to draw the graph. f(x) = x? + 100

> Determine an appropriate viewing rectangle for the given function and use it to draw the graph. f (x) = x3 – 225x

> Determine an appropriate viewing rectangle for the given function and use it to draw the graph. f (x) = √0.1x +20

> Determine an appropriate viewing rectangle for the given function and use it to draw the graph. f(x) = /81 - x*

> Determine an appropriate viewing rectangle for the given function and use it to draw the graph. f (x) = x3 + 15x2 +65x

> Determine an appropriate viewing rectangle for the given function and use it to draw the graph. f(x) — х2 — 36х + 32

> Use a graphing calculator or computer to determine which of the given viewing rectangles produces the most appropriate graph of the function f (x) = x4 – 16x2 + 20. (a) [-3, 3] by [-3, 3] (c) [-50, 50] by [-50, 50] (b) [-10, 10] by

> Use a graphing calculator or computer to determine which of the given viewing rectangles produces the most appropriate graph of the function f (x) = √x3 - 5x2. (a) [-5, 5] by [-5, 5] (b) [0, 10] by [0, 2] (c) [0, 10] by [0, 10]

> Determine an appropriate viewing rectangle for the given function and use it to draw the graph. y = 10sin x + sin100 x

> Graph the function by hand, not by plotting points, but by starting with the graph of one of the standard functions given in Section 1.2, and then applying the appropriate transformations. y = -x3

> Determine whether the curve is the graph of a function of x. If it is, state the domain and range of the function. 1 이 1

> The graph of y = √3x – x2 is given. Use transformations to create a function whose graph is as shown. y y=V3r -r 1.5+ 3 -4 -1 0 -2.5

> The graph of y = √3x – x2 is given. Use transformations to create a function whose graph is as shown. y y=V3r -r 1.5+ 3 y. 3+ 2 5

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

> Match each equation with its graph. Explain your choices. (Don’t use a computer or graphing calculator.) y 4 f (а) у %3D Зх (c) y = x' (b) y = 3" (а) у —

> Find the functions (a) f0g, (b) g0f, (c) f0f, and (d)g0g and their domains. f(4) =T g(x) = sin 2x 1 +x"

> Find the functions (a) f0g, (b) g0f, (c) f0f, and (d)g0g and their domains. f(x) = JE, g(x) = VT- x

> Find the functions (a) f0g, (b) g0f, (c) f0f, and (d)g0g and their domains. f(x) = 1 - 3x, g(x) = cos x

> Evaluate the difference quotient for the given function. Simplify your answer. x + 3 x + 1' f(x) – f(1) x - 1 f(x)

> The manager of a weekend flea market knows from past experience that if he charges dollars for a rental space at the market, then the number of spaces he can rent is given by the equation y = 200 - 4x. (a). Sketch a graph of this linear function. (Rememb

> The table shows the mean (average) distances d of the planets from the sun (taking the unit of measurement to be the distance from the earth to the sun) and their periods T (time of revolution in years). (a). Fit a power model to the data. (b). Kepler&

> Graph the function by hand, not by plotting points, but by starting with the graph of one of the standard functions given in Section 1.2, and then applying the appropriate transformations. y = |cos

> Graph the function by hand, not by plotting points, but by starting with the graph of one of the standard functions given in Section 1.2, and then applying the appropriate transformations. y = 1 + - 1

> Graph the function by hand, not by plotting points, but by starting with the graph of one of the standard functions given in Section 1.2, and then applying the appropriate transformations. y =}(x? + 8x)

> Graph the function by hand, not by plotting points, but by starting with the graph of one of the standard functions given in Section 1.2, and then applying the appropriate transformations. y = |x| - 2

> Graph the function by hand, not by plotting points, but by starting with the graph of one of the standard functions given in Section 1.2, and then applying the appropriate transformations. y = √x + 3

> Graph the function by hand, not by plotting points, but by starting with the graph of one of the standard functions given in Section 1.2, and then applying the appropriate transformations. y = 1/ x - 4

> Graph the function by hand, not by plotting points, but by starting with the graph of one of the standard functions given in Section 1.2, and then applying the appropriate transformations. y = 4 sin 3x

> Graph the function by hand, not by plotting points, but by starting with the graph of one of the standard functions given in Section 1.2, and then applying the appropriate transformations. y = x2 - 4x + 3

> Graph the function by hand, not by plotting points, but by starting with the graph of one of the standard functions given in Section 1.2, and then applying the appropriate transformations. y = 1 - x2

> Determine an appropriate viewing rectangle for the given function and use it to draw the graph. f(x) = sin Ja %3D

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

> What do all members of the family of linear functions f (x) = c - x have in common? Sketch several members of the family

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

> 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 of electricity us

> What do all members of the family of linear functions f (x) = 1 + m (x+3) have in common? Sketch several members of the family.

> 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 of the window. -r-

> Find a formula for the described function and state its domain. Express the surface area of a cube as a function of its volume.

> Find an expression for the function whose graph is the given curve. The top half of the circle x2 + (y – 2)2 = 4

> Find an expression for the function whose graph is the given curve. The line segment joining the points (-5, 10) and (7, -10).

> Find an expression for the function whose graph is the given curve. The line segment joining the points (1, -3) and (5, 7).

> The graph shows the height of the water in a bathtub as a function of time. Give a verbal description of what you think happened. height (inches) 15+ 10t time (min) 10 15 in

> Suppose the graph of f is given. Write equations for the graphs that are obtained from the graph of f as follows. (a). Shift 3 units upward. (b). Shift 3 units downward. (c). Shift 3 units to the right. (d). Shift 3 units to the left. (e). Reflect about

> What is the Pigou effect and how does it result in a downward-sloping aggregate demand curve?

> Explain the difference between movement down, or along, the aggregate demand curve and a shifting out of the aggregate demand curve.