Use a calculator to evaluate the trigonometric function. Round your answers to four decimal places. cos (–3π / 7)
> A pebble is dropped into a calm pond, causing ripples in the form of concentric circles. The radius (in feet) of the outer ripple is given by r(t) = 0.6t, where t is the time in seconds after the pebble strikes the water. The area of the circle is given
> Use the graphs of f and g to evaluate each expression. If the result is undefined, explain why. a. ( f ∘ g)(3) b. g(f(2)) c. g(f(5)) d. (f ∘ g)(−3) e. (g &
> Let f(x) = 1/ 1-x. a. What are the domain and range of f? b. Find the composition f( f(x)). What is the domain of this function? c. Find f( f( f(x))). What is the domain of this function? d. Graph f( f( f(x))). Is the graph a line? Why or why not?
> Find the composite functions f ∘ g and g ∘ f. Find the domain of each composite function. Are the two composite functions equal? f(x) = 1/x g(x) = √x + 2
> Find the composite functions f ∘ g and g ∘ f. Find the domain of each composite function. Are the two composite functions equal? f(x) = 3/x g(x) = x2 − 1
> Find the composite functions f ∘ g and g ∘ f. Find the domain of each composite function. Are the two composite functions equal? f(x) = x2 – 1 g(x) = −x
> Find the composite functions f ∘ g and g ∘ f. Find the domain of each composite function. Are the two composite functions equal? f(x) = x2 g(x) = √x
> Test for symmetry with respect to each axis and to the origin. xy2 = −10
> Given f(x) = 2x3 and g(x) = 4x + 3, evaluate each expression. a. f(g(0)) b. f (g( 1 2)) c. g(f(0)) d. g( f (−1 4)) e. f(g(x)) f. g( f(x))
> Given f(x) = √x and g(x) = x2 − 1, evaluate each expression. a. f(g(1)) b. g(f(1)) c. g(f(0)) d. f(g(−4)) e. f(g(x)) f. g(f(x))
> Find (a) f (x) + g(x), (b) f (x) − g(x), (c) f (x) ● g(x), and (d) f (x) g(x). f(x) = x2 + 5x + 4 g(x) = x + 1
> Find (a) f (x) + g(x), (b) f (x) − g(x), (c) f (x) ∙ g(x), and (d) f (x) g(x). f(x) = 2x – 5 g(x) = 4 − 3x
> Sketch the graph of the function f(x) = √x and label the point (4, 2) on the graph. a. Find the slope of the line joining (4, 2) and (9, 3). Is the slope of the tangent line at (4, 2) greater than or less than this number? b. Find the slope of the line j
> Use the graph of f shown in the figure to sketch the graph of each function. To print an enlarged copy of the graph, go to MathGraphs.com. a. f(x − 4) b. f(x + 2) c. f(x) + 4 d. f(x) − 1 e. 2f(x) f. 1 2 f(x) g. f
> Use the graph of f shown in the figure to sketch the graph of each function. To print an enlarged copy of the graph, go to MathGraphs.com. a. f(x + 3) b. f(x − 1) c. f(x) + 2 d. f(x) − 4 e. 3f(x) f. 1/4 f(x) g
> Use the graph of y = f (x) to match the function with its graph. y = f(x − 1) + 3
> Use the graph of y = f (x) to match the function with its graph. y = f(x + 6) + 2
> Use the graph of y = f (x) to match the function with its graph. y = −f(x − 4)
> Test for symmetry with respect to each axis and to the origin. xy = 4
> Determine whether the statement is true or false. If it is false, explain why or give an example that shows it is false. If the domain of a function consists of a single number, then its range must also consist of only one number.
> Use the graph of y = f (x) to match the function with its graph. y = −f(−x) − 2
> Use the graph of y = f (x) to match the function with its graph. y = f(x) − 5
> Use the graph of y = f (x) to match the function with its graph. y = f(x + 5)
> One of the fundamental themes of calculus is to find the slope of the tangent line to a curve at a point. To see how this can be done, consider the point (2, 4) on the graph of f(x) = x2 (see figure). a. Find the slope of the line joining (2, 4) and (3,
> The graph shows one of the six basic functions and a transformation of the function. Describe the transformation. Then use your description to write an equation for the transformation.
> The graph shows one of the six basic functions and a transformation of the function. Describe the transformation. Then use your description to write an equation for the transformation.
> The graph shows one of the six basic functions and a transformation of the function. Describe the transformation. Then use your description to write an equation for the transformation.
> The graph shows one of the six basic functions and a transformation of the function. Describe the transformation. Then use your description to write an equation for the transformation.
> Determine whether y is a function of x. x2 y − x2 + 4y = 0
> Determine whether y is a function of x. y2 = x2 − 1
> Test for symmetry with respect to each axis and to the origin. y = x3 + x
> Sketch the graph of the function. y = -4 csc 3x
> Sketch the graph of the function. y = -sec 2πx
> Sketch a graph of the function and find its domain and range. Use a graphing utility to verify your graph. h(x) = √x − 6
> Sketch the graph of the function. y = cot x/2
> Sketch the graph of the function. y = 1/3 tan x
> Sketch the graph of the function. y = 8 cos x/4
> Sketch the graph of the function. y = 3 sin 2x/5
> Sketch the graph of the function. y = sin πx
> Determine whether y is a function of x. x2 + y = 16
> Sketch the graph of the function. y = 9 cos x
> Solve the equation for θ, where 0 ≤ θ ≤ 2π 2 sec2 θ + tan2 θ − 5 = 0
> Evaluate the function at the given value(s) of the independent variable. Simplify the results. f(x) = 3x – 1 f(x) – f(1) / x - 1
> Solve the equation for θ, where 0 ≤ θ ≤ 2π sec2 θ − sec θ − 2 = 0
> You drive to the beach at a rate of 120 kilometers per hour. On the return trip, you drive at a rate of 60 kilometers per hour. What is your average speed for the entire trip? Explain your reasoning.
> Solve the equation for θ, where 0 ≤ θ ≤ 2π cos3 θ = cos θ
> Solve the equation for θ, where 0 ≤ θ ≤ 2π 2 sin2 θ + 3 sin θ + 1 = 0
> solve the equation for θ, where 0 ≤ θ ≤ 2π 2 cos2 θ = 1
> solve the equation for θ, where 0 ≤ θ ≤ 2π 2 cos θ + 1 = 0
> Use a calculator to evaluate the trigonometric function. Round your answers to four decimal places. sin (–π / 9)
> Use a calculator to evaluate the trigonometric function. Round your answers to four decimal places. csc 2π / 9
> Determine whether y is a function of x. x2 + y2 = 16
> Use a calculator to evaluate the trigonometric function. Round your answers to four decimal places. sec 12π / 5
> Test for symmetry with respect to each axis and to the origin. y2 = x3 − 8x
> You are in a boat 2 miles from the nearest point on the coast. You will travel to a point Q located 3 miles down the coast and 1 mile inland (see figure). You can row at 2 miles per hour and walk at 4 miles per hour. Write the total time T of the trip as
> Use a calculator to evaluate the trigonometric function. Round your answers to four decimal places. cot 401º
> Use a calculator to evaluate the trigonometric function. Round your answers to four decimal places. tan 33º
> Evaluate the sine, cosine, and tangent of the angle. Do not use a calculator. tan 33º
> Evaluate the sine, cosine, and tangent of the angle. Do not use a calculator. 405º
> Evaluate the sine, cosine, and tangent of the angle. Do not use a calculator. -4π/3
> Evaluate the sine, cosine, and tangent of the angle. Do not use a calculator. 13π/6
> Evaluate the sine, cosine, and tangent of the angle. Do not use a calculator. 240º
> Evaluate the sine, cosine, and tangent of the angle. Do not use a calculator. -45º
> Convert the radian measure to degree measure. -13π / 6
> Vertical Line Test to determine whether y is a function of x. To print an enlarged copy of the graph, go to MathGraphs.com. x2 + y2 = 4
> Find any intercepts. y = 4x2 + 3
> Sketch a graph of the function and find its domain and range. Use a graphing utility to verify your graph. f(t) = 2 / 7 + t
> Determine whether the statement is true or false. If it is false, explain why or give an example that shows it is false.
> Use a graphing utility to compare the graph of f(x) = 4/ π (sin πx + 1/3 sin 3 πx) with the given graph. Try to improve the approximation by adding a term to f(x). Use a graphing utility to verify that your new approximat
> The monthly sales S (in thousands of units) of a seasonal product are modeled by S = 58.3 + 32.5 cos πt/6 where t is the time (in months), with t = 1 corresponding to January. Use a graphing utility to graph the model for S and determine the months when
> The model for the height h of a Ferris wheel car is h = 51 + 50 sin 8πt where t is measured in minutes. (The Ferris wheel has a radius of 50 feet.) This model yields a height of 51 feet when t = 0. Alter the model so that the height of the car is 1 foot
> Sketch the graphs of f(x) = sin x, g(x) = │sin x│, and h(x) = sin(│x│). In general, how are the graphs of ∣f(x)∣ and f(∣x∣) related to the graph of f ?
> Consider an angle in standard position with r = 12 centimeters, as shown in the figure. Describe the changes in the values of x, y, sin θ, cos θ, and tan θ as θ increases continually from 0°
> How do the ranges of the cosine function and the secant function compare?
> Explain how to restrict the domain of the sine function so that it becomes a one-to-one function.
> You are given the value of tan θ. Is it possible to find the value of sec θ without finding the measure of θ? Explain.
> Sketch a graph of the function and find its domain and range. Use a graphing utility to verify your graph. g(x) = 1 / x2 + 2
> Find any intercepts. y = 2x – 5
> Find a, b, and c such that the graph of the function matches the graph in the figure. y = a sin(bx − c)
> Find a, b, and c such that the graph of the function matches the graph in the figure. y = a cos(bx − c)
> Sketch the graph of the function. y = 1 + sin(x + π/2)
> Sketch the graph of the function. y = 1 + cos(x – π/2)
> Sketch the graph of the function. y = cos(x – π/3)
> Sketch the graph of the function. y = sin(x + π)
> Sketch the graph of the function. y = csc 2πx
> Sketch the graph of the function. y = 2 sec 2x
> Sketch the graph of the function. y = tan 2x
> Sketch the graph of the function. y = csc x/2
> Use a graphing utility to graph the equation. Move the cursor along the curve to approximate the unknown coordinate of each solution point accurate to two decimal places. y = x5 − 5x (−0.5, y) (x, −4)
> Sketch a graph of the function and find its domain and range. Use a graphing utility to verify your graph. f (x) = x2 + 5
> Sketch the graph of the function. y = 2 tan x
> Sketch the graph of the function. y = -sin 2πx/3
> Sketch the graph of the function. y = sin x/2
> Sketch the graph of the function. y = sin x/2
> Use a graphing utility to graph each function f in the same viewing window for c = −2, c = −1, c = 1, and c = 2. Give a written description of the change in the graph caused by changing c. a. f(x) = sin x + c b. f(x) = -sin (2πx - c) c. f(x) = c cos x
> Use a graphing utility to graph each function f in the same viewing window for c = −2, c = −1, c = 1, and c = 2. Give a written description of the change in the graph caused by changing c. a. f(x) = c sin x b. f(x) = cos(cx) c. f(x) = cos(πx − c)
> Find the period of the function. y = csc 4x
> Find the period of the function. y = sec 5x
> Find the period of the function. y = 7 tan 2πx
> Use a graphing utility to graph the equation. Move the cursor along the curve to approximate the unknown coordinate of each solution point accurate to two decimal places. y = √5 − x (2, y) (x, 3)
