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Given the rational function. f(x)= \frac {3x+4}{-5x+8}. Determine the following: a. Where the vertical asymptote occurs? b. At what point x intercept occurs? c. At what point y intercept occurs? d. Where the non vertical asymptote occurs? e. Draw the gr
Draw the graph for the following function: f(x)= \frac{2-x}{3+x}
Solve the following rational equations. a) \frac{1}{3a + 18} = 1 - \frac{8}{a + 6} b) \frac{7}{2x^2 - x - 1} = \frac{5}{x - 1}
Let f(x) \frac{2x^2-4}{x^2-3}. a. State the y intercept b. State the x intercept(s) c. State the vertical asymptote(s) d. State the horizontal asymptote
Solve. x^\frac{-1}{2}(x + 9)^\frac{1}{2} + x^\frac{1}{2}(x + 9)^\frac{-1}{2}
Find the partial fractions decomposition and an antiderivative. \frac{x + 2}{x^3 + x}
Suppose that in order to remove x% of the pollution from the oil spill, it costs C(x) = \frac{15x}{100-x} thousands of dollars. a. How much does it cost to remove 25% of the pollution? b. How much does it cost to remove 50% of the pollution?
Simplify the following. y = \frac{x}{4 - \sqrt{16 + x})}
For the given rational function f(x) = \frac{x^2-x+6 }{x^2-2x-3} \\ a) Find the domain of f. \\ b) Identify any vertical asymptotes of the graph of y=f(x). \\ c) Identify any holes in the graph. \\ d) Find the horizontal and/or slant asymptote, if they
Let f(x) = \frac{3x - 9}{x - 2} (a) state the domain (b) state the vertical asymptote(s) (c) State the horizontal asymptote (d) state the graph
Maria bought seven boxes. a week later half of all her boxes were destroyed in a fire. there are now only 22 boxes left. with how many did she start with?
Find the excluded value of the fraction. \frac{x + 11}{3x^2 + 5x - 2}
Simplify the rational expression. State any excluded values. \frac{7x - 14}{x - 2} A. x B. 7; where x is not equal to -7 C. 7; where x is not equal to 2 D. 0
What is the domain and range, x- and y-intercept, and horizontal and vertical asymptote of y = \frac{400 + 40x}{x}?
Which is a rational function? a) Y = \frac{x - 3}{x^2} \\ b) Y = 2x \\ c) Y = \frac{x - 5}{2} \\ d) Y = x^2 - x + 4
Draw a rough picture of the following surface and also clarify some basic geometric properties (e.g. axis, vertex): x^2 + 2z^2 - y^2 = 1.
Draw a rough picture of the following surface and also clarify some basic geometric properties (e.g. axis, vertex): x^2 + z^2 = 4.
Find the excluded value for the following. \frac{12a}{a^2 - 3a - 10}
Find the domain of the real valued rational function f given below. f(x) = \frac{(x - 1) }{ (x - 3)}
Find all numbers for which the rational expression is undefined. \frac{7}{3v + 7}
Simplify and find the excluded values. \frac{15x^2}{15x + 10}
(a) What is wrong with the following equation? x^2 + x - 6/x - 2 = x + 3 (b) In view of part (a), explain why the equation lim x -> 2 (x^2 + x - 6/x - 2) = lim x -> 2 (x+3) is correct.
If f(x)= p(x) \ / \ q(x) and period of p(x) \text{ is } T_1 \text{ and period of } q(x) \text{ is } T_2 then find the period of f(x) .
Use a graphing utility with the specified viewing window to find the points of intersection of the graphs of the following functions. f(x) = 5x - 1, g(x) = x^2 - 2; [-4, 9]\; \text{by}\; [-6, 30] Sele
Find a formula for a function f that satisfies the following conditions. \lim_{x \rightarrow \pm\infty},f(x)=0\lim_{x \rightarrow 0 },f(x)=-\infty, \\ , \\ \lim_{x \rightarrow 9^{-}},f(x)=\infty
What numbers for which the rational expression is undefined? \frac{8}{9x + 7}
What are the excluded values of the function? y=\frac{5}{(6x-72)}
Write a complete approach statement for y = fraction {(2x + 1)(2 - x)}{2x + 1}.
Analyze the graph of f(x)=\frac{2(x^{2}-9)}{x^{4}-4}
Analyze the function f(x)= (x^3-4x^2-31x+70)/(x^2-5x+6). Find the y-intercept, the x-intercept(s), the removable singularities, the vertical asymptotes and the horizontal asymptotes.
A certain factory, the daily output is Q(K,L)=60K^{1/2}L^{1/3} units, where K denotes the capital investment measured in units of $1,000 and L the size of the labor force measured in worker-hours. The
Create a function with the following properties: a. It has a horizontal asymptote at y= 2. b. It has a discontinuity at x= 2 which is not a vertical asymptote. c. It has no other discontinuities or a
Sketch the graph of F(x)=\frac{x^2}{x-1} . Identify asymptotes, extrema, points of inflection and / or axis intercepts.
Sketch the function f(x) = x \sqrt{2+x} Investigate the following graphical information a. Domain b. Intercepts c. Symmetry d. Asymptotes e. Concavity and points of inflection
Find the possible formula for the function in the figure below. (Graph)
Analyze and sketch a graph of the function f(x) = fraction {x}{x+1}
Let f(x) = x^2 and g(x) = x^3. Use these graphs to sketch the graph of the following functions. A) h(x) = -(x - 1)^2 + 2 B) p(x) = (3 - x)^3 - 4
Consider the functions f(x) = \ln \frac{\sqrt {x^2+1}}{x} and g(x) = \frac{1}{2} \ln(x^2 + 1) - \ln(x) . Graph f and g. What is the relationship between the graphs and therefore between the function
In 1774, Captain James Cook left 10 rabbits on a small Pacific island. The rabbit population is approximated by P(t)= \frac{2000}{1 + e^{5.3 - 0.4t}} with t measured in years since 1774. Use a calcula
Is \frac{x^4}{8} + \frac{5}{x} a rational function? If it is, write it as \frac{p(x)}{q(x)} where p(x) and q(x) are polynomials with no common factor.
Sketch the graph of the following function. Indicate where the function is increasing or decreasing, where any relative extrema occur, where asymptotes occur, where the graph is concave up or concave
Find: 1. The graph of f is given. State the numbers at which f is not differentiable. Image src='annotation_2019-07-31_1518081039845790348880442.png' alt='' caption='' 2. Use the given graph to estima
Consider the function below. f (x) = \frac{x^2}{x^2 - 16} (a) Find the vertical and horizontal asymptotes. (b) Find the interval where the function is Increasing. Find the interval where the func
f(x) = fraction {x}{square root {x^2 + 3} - 2x } find the verticle asymptotes of f(x) Find the horizontal asymptotes of f(x), make sure with both direction of the x-axis.
How do you find the vertical asymptotes of a rational function when the denominator is in factored form?
Sketch the level curves, z = 1 & z = 4 for the function f(x, y) = x^{1 / 3} y^{2 / 3}, x greater than 0, y greater than 0.
1. If f(x) =\frac{x^2+1}{x^2-1}, find the value(s) of x where the graph of f has a horizontal tangents. 2. Prove the quotient rule using the product rule and the chain rule. 3. Simplify the following
Consider f(x) = \frac{2x^2 - 8}{x^2 - 5x - 6} \\ (a) Find the domain for this function.\\ (b) Find the x - and y-intercepts.\\ (c) Find the horizontal and vertical asymptotes.
sketch the curve. y = fraction {x}{x^2 - 16}
Write an equation for the function graphed below.
Make a complete graph of f(x) = \frac{x^2}{x+3}
Sketch a graph of the function. List any extrema, and indicate any asymptotes or points of inflection. f (x) = {x + 1} / {x - 2}.
Consider the following. \\ g(x) = \frac{x^2 - x -6}{x^2 - 16}\\ (a) State the domain of the function.\\ (b) Identify all intercepts. \\ (c) Find any vertical and horizontal asymptotes.
Give an example of a rational function f(x) that is continuous for all values of x except at x = \frac{+}{-5} , where it has non-removable discontinuities, and at x = 2, where it has a removable disc
Find all discontinuities of the function g(x) = \frac{2x^2 - 14x + 24}{3x^2 - 6x - 9} . Use limits to determine what type each discontinuity is.
Consider the function f(x) = \frac{x^2}{(x-2)^2} a. Find the horizontal and vertical asymptotes. b. Find the intervals of increase and decrease. c. Find the intervals where the function is concave
Write the function with a hole at x = 4 , a horizontal asymptote at y = 2 , and a vertical asymptote at x = - 1
Let f(x) = frac{40x^2 - 2x + 1}{x^3 - 3x^2 + 2x} . Find the domain of f(x) . Find the horizontal and vertical asymptotes.
Determine, with reason, if each statement is true or false. (a) The function {x^4 + x - 1} / {x^3 - 4 x + 9} is a proper rational function. (b) The polynomial x^3 + 5 x^2 + 4 x has only simple, linear
Let \ f'(x) = \frac {-1(x+3)(x-1)}{(x+4)} Find all intervals for which f is increasing. Label the x-value for all relative extreme.
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