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8th Edition

James Stewart

Publisher: Cengage Learning

ISBN: 9781305270336

Chapter 1, Problem 11RCC

Textbook Problem

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Suppose the graph of *f* is given. Write an equation for each of the graphs that are obtained from the graph of *f* as follows.

(a) Shift 2 units upward.

(b) Shift 2 units downward.

(c) Shift 2 units to the right.

(d) Shift 2 units to the left.

(e) Reflect about the *x*-axis.

(a)

To determine

**To write:** The equation of the graph which is obtained from the given graph such that the graph is shifted 2 units upward.

Let the equation of the graph be

Since the graph is vertically (upward) shifted, add 2 to the

(b)

To determine

**To write:** The equation of the graph which is obtained from the given graph such that the graph is shifted 2 units downward.

(c)

To determine

**To write:** The equation of the graph which is obtained from the given graph such that the graph is shifted 2 units to the right side.

(d)

To determine

**To write:** The equation of the graph which is obtained from the given graph such that the graph is shifted 2 units to the left side.

(e)

To determine

**To write:** The equation of the graph which is obtained from the given graph such that the graph reflects about the *x* axis.

(f)

To determine

**To write:** The equation of the graph which is obtained from the given graph such that the graph reflects about the *y* axis.

(g)

To determine

**To write:** The equation of the graph which is obtained from the given graph such that the graph stretched vertically by a factor of 2.

(h)

To determine

**To write:** The equation of the graph which is obtained from the given graph such that the graph shrunk vertically by a factor of 2.

(i)

To determine

**To write:** The equation of the graph which is obtained from the given graph such that the graph stretched horizontally by a factor of 2.

(j)

To determine

**To write:** The equation of the graph which is obtained from the given graph such that the graph shrunk horizontally by a factor of 2.

Single Variable Calculus: Early Transcendentals

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F(x) =...Ch. 1.3 - Express the function in the form f g. 44. F(x) =...Ch. 1.3 - Express the function in the form f g. 45....Ch. 1.3 - Express the function in the form f g. 46....Ch. 1.3 - Express the function in the form f g. 47. v(t) =...Ch. 1.3 - Express the function in the form f g. 48....Ch. 1.3 - Express the function in the form f g h. 49....Ch. 1.3 - Express the function in the form f g h. 50....Ch. 1.3 - Express the function in the form f g h. 51. S(t)...Ch. 1.3 - Use the table to evaluate each expression. (a)...Ch. 1.3 - Use the given graphs of f and g to evaluate each...Ch. 1.3 - Use the given graphs of f and g to estimate the...Ch. 1.3 - A stone is dropped into a lake, creating a...Ch. 1.3 - A spherical balloon is being inflated and the...Ch. 1.3 - A ship is at a speed of 30km/h parallel to a...Ch. 1.3 - An airplane is flying at a speed of 350 mi/h at an...Ch. 1.3 - The Heaviside function H is defined by It is used...Ch. 1.3 - The Heaviside function defined in Exercise 59 can...Ch. 1.3 - Let f and g be linear functions with equations...Ch. 1.3 - If you invest x dollars at 4% interest compounded...Ch. 1.3 - (a) If g(x) = 2x + 1 and h(x) = 4x2 + 4x + 7, find...Ch. 1.3 - If f(x) = x + 4 and h(x) = 4x 1, find a function...Ch. 1.3 - Suppose g is an even function and let h =f g. Is...Ch. 1.3 - Suppose g is an odd function and let h = f g. 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(a)...Ch. 1.5 - Express the given quantity as a single logarithm....Ch. 1.5 - Express the given quantity as a single logarithm....Ch. 1.5 - Express the given quantity as a single logarithm....Ch. 1.5 - Use Formula 10 to evaluate each logarithm correct...Ch. 1.5 - Use Formula 10 to graph the given functions on a...Ch. 1.5 - Use Formula 10 to graph the given functions on a...Ch. 1.5 - Suppose that the graph of y = log2 x is drawn on a...Ch. 1.5 - Compare the functions f(x)=x0.1 and g(x) = ln x by...Ch. 1.5 - Make a rough sketch of the graph of each function....Ch. 1.5 - Make a rough sketch of the graph of each function....Ch. 1.5 - (a) What are the domain and range of f? (b) What...Ch. 1.5 - (a) What are the domain and range of f? (b) What...Ch. 1.5 - Solve each equation for x. 51. (a) e74x=6 (b)...Ch. 1.5 - Solve each equation for x. 52. (a) ln(x2 1) = 3...Ch. 1.5 - Solve each equation for x. 53. (a) 2x5 = 3 (b) ln...Ch. 1.5 - Solve each equation for x. 54. (a) ln(ln x) = 1...Ch. 1.5 - Solve each inequality for x. 55. (a) ln x 0 (b)...Ch. 1.5 - Solve each inequality for x. 56. (a) 1 e3x1 2...Ch. 1.5 - (a) Find the domain of f(x) = ln(ex 3). (b) Find...Ch. 1.5 - (a) What are the values of eln 300 and ln(e300)?...Ch. 1.5 - If a bacteria population starts with 100 bacteria...Ch. 1.5 - When a camera flash goes off, the batteries...Ch. 1.5 - Find the exact value of each expression. 63. (a)...Ch. 1.5 - Find the exact value of each expression. 64. (a)...Ch. 1.5 - Find the exact value of each expression. 65. (a)...Ch. 1.5 - Find the exact value of each expression. 66. (a)...Ch. 1.5 - Find the exact value of each expression. 67. (a)...Ch. 1.5 - Find the exact value of each expression. 68. (a)...Ch. 1.5 - Prove that cos(sin1x)=1x2.Ch. 1.5 - Simplify the expression. 70. tan(sin1 x)Ch. 1.5 - Simplify the expression. 71. sin(tan1 x)Ch. 1.5 - Simplify the expression. 72. sin(2 arccos x)Ch. 1.5 - Graph the given functions on the same screen. 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How can you...Ch. 1 - (a) How is the inverse sine function f(x) = sin1 x...Ch. 1 - Determine whether the statement is true or false....Ch. 1 - Determine whether the statement is true or false....Ch. 1 - Determine whether the statement is true or false....Ch. 1 - Determine whether the statement is true or false....Ch. 1 - Determine whether the statement is true or false....Ch. 1 - Determine whether the statement is true or false....Ch. 1 - Determine whether the statement is true or false....Ch. 1 - Determine whether the statement is true or false....Ch. 1 - Determine whether the statement is true or false....Ch. 1 - Determine whether the statement is true or false....Ch. 1 - Determine whether the statement is true or false....Ch. 1 - Determine whether the statement is true or false....Ch. 1 - Determine whether the statement is true or false....Ch. 1 - Determine whether the statement is true or false....Ch. 1 - Let f be the function whose graph is given. (a)...Ch. 1 - The graph of g is given. (a) State the value of...Ch. 1 - lf f(x) = x2 2x + 3, evaluate the difference...Ch. 1 - Sketch a rough graph or the yield of a crop as a...Ch. 1 - Find the domain and range of the function. Write...Ch. 1 - Find the domain and range of the function. Write...Ch. 1 - Find the domain and range of the function. Write...Ch. 1 - Find the domain and range of the function. Write...Ch. 1 - Suppose that the graph of .f is given. Describe...Ch. 1 - The graph of .f is given. Draw the graphs of the...Ch. 1 - Use transformations to sketch the graph of the...Ch. 1 - Use transformations to sketch the graph of the...Ch. 1 - Use transformations to sketch the graph of the...Ch. 1 - Use transformations to sketch the graph of the...Ch. 1 - Use transformations to sketch the graph of the...Ch. 1 - Use transformations to sketch the graph of the...Ch. 1 - Determine whether f is even, odd, or neither even...Ch. 1 - Find an expression for the function whose graph...Ch. 1 - If f(x) = In x and g(x) = x2 9. find the...Ch. 1 - Express the function F(x)=1/x+x as a composition...Ch. 1 - A small-appliance manufacturer finds that it costs...Ch. 1 - If f(x) = 2x + In x, find f1(2).Ch. 1 - Find the inverse function of f(x)=x+12x+1.Ch. 1 - Find the exact value of each expression. 64. (a)...Ch. 1 - Solve each equation for x. (a) ex = 5 (b) ln x = 2...Ch. 1 - The half-life of palladium-100, 100Pd, is four...Ch. 1 - The population of a certain species in a limited...Ch. 1 - One of the legs of a right triangle has length 4...Ch. 1 - The altitude perpendicular to the hypotenuse of a...Ch. 1 - Solve the equation |2x 1| |x + 5| = 3.Ch. 1 - Solve the inequality |x 1| |x 3| 5.Ch. 1 - Sketch the graph of the function f(x) = |x2 4| x...Ch. 1 - Sketch the graph of the function g(x) = |x2 1 | ...Ch. 1 - Draw the graph of the equation x + |x| = y + |y|.Ch. 1 - Sketch the region in the plane consisting of all...Ch. 1 - The notation max{a, b, } means the largest of the...Ch. 1 - Sketch the region in the plane defined by each of...Ch. 1 - Evaluate (log2 3)(log3 4)(log4 5)(log31 32).Ch. 1 - (a) Show that the function f(x)=ln(x+x2+1) is an...Ch. 1 - Solve the inequality ln(x2 2x 2) 0.Ch. 1 - Use indirect reasoning to prove that log2 5 is an...Ch. 1 - A driver sets out on a journey. For the first half...Ch. 1 - Is it true that f(g+h)=fg+fh?Ch. 1 - Prove that if n is a positive integer, then 7n 1...Ch. 1 - Prove that 1 + 3 + 5 + + (2n l ) = n2.Ch. 1 - If fo(x) = x2 and fn+1(x) = fo(fn(x)) for n = 0,...Ch. 1 - (a) If fo(x)=12x and fn+1=fofnforn=0,1,2,, find an...

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âŸ¨3, âˆ’4âŸ©
âŸ¨4, âˆ’3âŸ©

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yâ€² + xey = ex+y is separable.

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