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Chapter 2: Problem 32
Solve each polynomial inequality and graph the solution set on a real number line. Express each solution set in interval notation. $$x(4-x)(x-6) \leq 0$$
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a. If \(y=k x^{2},\) find the value of \(k\) using \(x=2\) and \(y=64\). b. Substitute the value for \(k\) into \(y=k x^{2}\) and write the resulting equation. c. Use the equation from part (b) to find \(y\) when \(x=5\).
Determine whether each statement makes sense or does not make sense, and explain your reasoning. I'm solving a polynomial inequality that has a value for which the polynomial function is undefined.
Use transformations of \(f(x)=\frac{1}{x}\) or \(f(x)=\frac{1}{x^{2}}\) to graph each rational function. $$h(x)=\frac{1}{(x-3)^{2}}+2$$
Determine whether each statement makes sense or does not make sense, and explain your reasoning. When solving \(f(x)>0,\) where \(f\) is a polynomial function, I only pay attention to the sign of \(f\) at each test value and not the actual function value.
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 \(g.\) $$g(x)=\frac{3 x-7}{x-2}$$
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