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Chapter 2: Problem 1
Find the domain of each rational function. $$f(x)=\frac{5 x}{x-4}$$
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Use long division to rewrite the equation for \(g\) in the form $$\text {quotient }+\frac{\text {remainder}}{\text {divisor}}$$ Then use this form of the function's equation and transformations of \(f(x)=\frac{1}{x}\) to graph \(g.\) $$g(x)=\frac{2 x-9}{x-4}$$
Write the equation of a rational function \(f(x)=\frac{p(x)}{q(x)}\) having the indicated properties, in which the degrees of p and q are as small as possible. More than one correct function may be possible. Graph your function using a graphing utility to verify that it has the required properties. \(f\) has a vertical asymptote given by \(x=1,\) a slant asymptote whose equation is \(y=x, y\) -intercept at \(2,\) and \(x\)-intercepts at -1 and 2.
Determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. Write a rational inequality whose solution set is \((-\infty,-4) \cup[3, \infty)\).
Determine whether each statement makes sense or does not make sense, and explain your reasoning. Using the language of variation, I can now state the formula for the area of a trapezoid, \(A=\frac{1}{2} h\left(b_{1}+b_{2}\right),\) as, "A trapezoid's area varies jointly with its height and the sum of its bases."
In a hurricane, the wind pressure varies directly as the square of the wind velocity. If wind pressure is a measure of a hurricane's destructive capacity, what happens to this destructive power when the wind speed doubles?
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