Find the points of intersection of the graphs of the equations. 5x + 3y = −1 x – y = -5
> Find the composite functions f ∘ g and g ∘ f. Find the domain of each composite function. Are the two composite functions equal? f(x) = 3x + 1 g(x) = −x
> What is the minimum degree of the polynomial function whose graph approximates the given graph? What sign must the leading coefficient have? a. / b. / c. / d. /
> Use a graphing utility to graph f(x) = x3 − 3x2. Use the graph to write a formula for the function g shown in the figure. a. / b. /
> Determine whether y is a function of x. x = 9 – y2
> Determine whether y is a function of x. xy + x3 – 2y = 0
> Use the 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 - y = 0
> Use the Vertical Line Test to determine whether y is a function of x. To print an enlarged copy of the graph, go to MathGraphs.com. x + y2 = 2
> A rancher plans to fence a rectangular pasture adjacent to a river. The rancher has 100 meters of fencing, and no fencing is needed along the river (see figure). a. Write the area A of the pasture as a function of x, the length of the side parallel to th
> Sketch a graph of the function and find its domain and range. Use a graphing utility to verify your graph. g(x) = √x + 1
> Sketch a graph of the function and find its domain and range. Use a graphing utility to verify your graph. f(x) = 4 / 2x – 1
> Find any intercepts. y = 2x − √x2 + 1
> Find the domain and range of the function. h(x) = 2 / x + 1
> 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 – 4) − y = 0
> Find the domain and range of the function. f(x) = -│x + 1│
> Find the domain and range of the function. g(x) = √6 - x
> Find the domain and range of the function. f(x) = x2 + 3
> Evaluate the function at the given value(s) of the independent variable. Simplify the results. f(x) = 2x - 6 f(x) – f(1) / x - 1
> Evaluate the function at the given value(s) of the independent variable. Simplify the results. f(x) = 4x2 f(x + ∆x) – f(x) / ∆x
> Consider the graph of the function f shown below. Use this graph to sketch the graphs of the following functions. To print an enlarged copy of the graph, go to MathGraphs.com. a. f(x + 1) b. f(x) + 1 c. 2f(x) d. f(−x) e. âˆ&#
> Evaluate the function at the given value(s) of the independent variable. Simplify the results. f(x) = x3 – 2x f(-3) f(2) f(-1) f(c - 1)
> Evaluate the function at the given value(s) of the independent variable. Simplify the results. f(x) = 5x + 4 f(0) f(5) f(-3) f(t + 1)
> A contractor purchases a piece of equipment for $36,500 that costs an average of $9.25 per hour for fuel and maintenance. The equipment operator is paid $13.50 per hour, and customers are charged $30 per hour. Write a linear equation for the cost C of op
> Find any intercepts. x2 y − x2 + 4y = 0
> The purchase price of a new machine is $12,500, and its value will decrease by $850 per year. Use this information to write a linear equation that gives the value V of the machine t years after it is purchased. Find its value at the end of 3 years.
> Find equations of the lines passing through (2, 4) and having the following characteristics. a. Slope of – (2/3) b. Perpendicular to the line x + y =0 c. Parallel to the line 3x – y =0 d. Parallel to the x-axis
> Vertical Line Test to determine whether y is a function of x. To print an enlarged copy of the graph, go to MathGraphs.com. x − y2 = 0
> Find equations of the lines passing through (−3, 5) and having the following characteristics. a. Slope of 7/16 b. Parallel to the line 5x – 3y = 3 c. Perpendicular to the line 3x + 4y = 8 d. Parallel to the y-axis
> Find an equation of the line that passes through the points. Then sketch the line. (-5, 5), (10, -1)
> The Heaviside function H(x) is widely used in engineering applications. a. H(x) – 2 b. H(x − 2) c. −H(x) d. H(−x) e. 1/2H(x) f. −H(x − 2) + 2
> Find an equation of the line that passes through the points. Then sketch the line. (0, 0), (8, 2)
> Sketch the graph of the equation. 3x + 2y = 12
> Sketch the graph of the equation. y = 4x – 2
> Sketch the graph of the equation. x = -3
> Find any intercepts.
> Sketch the graph of the equation. y = 6
> Find the slope and the y-intercept (if possible) of the line. 9 - y = x
> Find the slope and the y-intercept (if possible) of the line. y – 3x = 5
> Find an equation of the line that passes through the point and has the indicated slope. Then sketch the line. Point: (5, 4) Slope: m = 0
> Sketch a graph of the function and find its domain and range. Use a graphing utility to verify your graph. f(x) = x + √4 − x2
> There are two tangent lines from the point (0, 1) to the circle x2 + (y + 1)2 = 1 (see figure). Find equations of these two lines by using the fact that each tangent line intersects the circle at exactly one point. /
> Find an equation of the line that passes through the point and has the indicated slope. Then sketch the line. Point: (-3, 0) Slope: m = - 2/3
> Find an equation of the line that passes through the point and has the indicated slope. Then sketch the line. Point: (-8, 1) Slope: m is undefined
> Find an equation of the line that passes through the point and has the indicated slope. Then sketch the line. Point: (3, -5) Slope: m = 7/4
> Plot the pair of points and find the slope of the line passing through them. (-7, 8) , (-1, 8)
> Plot the pair of points and find the slope of the line passing through them. (3/2, 1) , (5, 5/2)
> Find any intercepts.
> Find the points of intersection of the graphs of the equations. x2 + y2 = 1 -x + y = 1
> Find the points of intersection of the graphs of the equations. x − y = −5 x2 – y = 1
> Find the points of intersection of the graphs of the equations. 2x + 4y = 9 6x – 4y = 7
> Consider the circle x2 + y2 − 6x − 8y = 0 as shown in the figure. Find the center and radius of the circle. Find an equation of the tangent line to the circle at the point (0, 0). Find an equation of the tangent line t
> Find any intercepts and test for symmetry. Then sketch the graph of the equation. y = │x − 4│ − 4
> Sketch a graph of the function and find its domain and range. Use a graphing utility to verify your graph. f(x) = √9 − x2
> Find any intercepts and test for symmetry. Then sketch the graph of the equation. y = 2 √4-x
> Find any intercepts and test for symmetry. Then sketch the graph of the equation. y2 = 9 – x
> Find any intercepts and test for symmetry. Then sketch the graph of the equation. y = 9x − x3
> Find any intercepts and test for symmetry. Then sketch the graph of the equation. y = −x2 + 4
> Find any intercepts. y = (x − 1)√x2 + 1
> Determine whether the statement is true or false. If it is false, explain why or give an example that shows it is false. The graph of a function of x cannot have symmetry with respect to the x-axis.
> Find any intercepts and test for symmetry. Then sketch the graph of the equation. y = −1/2x + 3
> Test for symmetry with respect to each axis and to the origin. xy = −2
> The function y = 3 cos(x/3) has a period that is three times that of the function y = cos x.
> Test for symmetry with respect to each axis and to the origin. y2 = x2 – 5
> Test for symmetry with respect to each axis and to the origin. y = x4 − x2 + 3
> Test for symmetry with respect to each axis and to the origin. y = x2 + 4x
> Amplitude is always positive.
> Find any intercepts. y = (x-3) √x + 4
> Plot the pair of points and find the slope of the line passing through them. (4, 6), (4, 1)
> Plot the pair of points and find the slope of the line passing through them. (0, 0), (-2, 3)
> Plot the pair of points and find the slope of the line passing through them. (3, −4), (5, 2)
> Estimate the slope of the line from its graph.
> Estimate the slope of the line from its graph.
> Estimate the slope of the line from its graph.
> Estimate the slope of the line from its graph.
> Sketch a graph of the function and find its domain and range. Use a graphing utility to verify your graph. f(x) = 1/4 x3 + 3
> Is it possible for two lines with positive slopes to be perpendicular? Why or why not?
> In the form y = mx + b, what does m represent? What does b represent?
> Match the equation with its graph. [The graphs are labeled (a), (b), (c), and (d).] y = -(3/2) x + 3
> Determine whether the statement is true or false. If it is false, explain why or give an example that shows it is false. If b2 − 4ac = 0 and a ≠ 0, then the graph of y = ax2 + bx + c has only one x-intercept.
> Determine whether the statement is true or false. If it is false, explain why or give an example that shows it is false. If b2 − 4ac > 0 and a ≠ 0, then the graph of y = ax2 + bx + c has two x-intercepts.
> Determine whether the statement is true or false. If it is false, explain why or give an example that shows it is false. If (−4, −5) is a point on a graph that is symmetric with respect to the y-axis, then (4, −5) is also a point on the graph.
> Determine whether the statement is true or false. If it is false, explain why or give an example that shows it is false. If (−4, −5) is a point on a graph that is symmetric with respect to the x-axis, then (4, −5) is also a point on the graph.
> Use the graphs of the two equations to answer the questions below. What are the intercepts for each equation? Determine the symmetry for each equation. Determine the point of intersection of the two equations.
> A graph is symmetric with respect to one axis and to the origin. Is the graph also symmetric with respect to the other axis? Explain
> A graph is symmetric with respect to the x-axis and to the y-axis. Is the graph also symmetric with respect to the origin? Explain.
> Find any intercepts. y = x-3 / x-4
> Write an equation whose graph has intercepts at x = −(3/2), x = 4, and x = 5 /2. (There is more than one correct answer.)
> For what values of k does the graph of y2 = 4kx pass through the point? a. (1, 1) b. (2, 4) c. (0, 0) d. (3, 3)
> How can you check that an ordered pair is a point of intersection of two graphs?
> Find the sales necessary to break even (R = C) when the cost C of producing x units is C = 2.04x + 5600 and the revenue R from selling x units is R = 3.29x.
> The table shows the numbers of cell phone subscribers (in millions) in the United States for selected years. (Source: CTIA-The Wireless Association) Use the regression capabilities of a graphing utility to find a mathematical model of the form y = at2
> The table shows the Gross Domestic Product, or GDP (in trillions of dollars), for 2009 through 2014. (Source: U.S. Bureau of Economic Analysis) Use the regression capabilities of a graphing utility to find a mathematical model of the form y = at + b fo
> Use a graphing utility to find the points of intersection of the graphs of the equations. Check your results analytically. y = -│2x - 3│ + 6 y = 6 - x
> Use a graphing utility to find the points of intersection of the graphs of the equations. Check your results analytically. y = √x+6 y = √-x2 -4x
> Use a graphing utility to find the points of intersection of the graphs of the equations. Check your results analytically. y = x4 − 2x2 + 1 y = 1 − x2
> Find any intercepts. y = x2 − 8x + 12
> Use a graphing utility to find the points of intersection of the graphs of the equations. Check your results analytically. y = x3 − 2x2 + x – 1 y = −x2 + 3x – 1
> Find the points of intersection of the graphs of the equations. x2 + y2 = 16 x + 2y = 4
> Find the points of intersection of the graphs of the equations. x2 + y2 = 5 x – y = 1
> Describe how to find the x- and y-intercepts of the graph of an equation.
> Find the points of intersection of the graphs of the equations. x = 3 − y2 y = x – 1
