91Ó°ÊÓ

Provide a short answer to each question. Do not use a calculator. What is the equation of the vertical asymptote of the graph of \(y=\frac{1}{(x+2)^{2}}-4 ? \quad\) of the horizontal asymptote?

Match the rational function in Column I with the appropriate description in Column II. Choices in Column II can be used only once. Do not use a calculator. (Column II) A. The \(x\) -intercept is \((-3,0)\) B. The \(y\) -intercept is \((0,5)\) C. The horizontal asymptote is \(y=4\) D. The vertical asymptote is \(x=-1\) E. There is a hole in its graph at \(x=-4\) F. The graph has an oblique asymptote. G. The \(x\) -axis is its horizontal asymptote. H. The \(y\) -axis is its vertical asymptote. (Column I) $$f(x)=\frac{4 x+3}{x-7}$$

Use a hand-drawn graph to explain why \(\sqrt{x}=-x-5\) has no real solutions.

Check that proposed solutions \(\frac{3}{2}\) and \(\frac{5}{3}\) from Example 6 are solutions of \(15 x^{-2}-19 x^{-1}+6=0\)

Evaluate each expression. Do not use a calculator. $$125^{-2 / 3}$$

Provide a short answer to each question. Do not use a calculator. Is \(f(x)=\frac{1}{x^{2}}\) an even or odd function? What symmetry does its graph exhibit?

Match the rational function in Column I with the appropriate description in Column II. Choices in Column II can be used only once. Do not use a calculator. (Column II) A. The \(x\) -intercept is \((-3,0)\) B. The \(y\) -intercept is \((0,5)\) C. The horizontal asymptote is \(y=4\) D. The vertical asymptote is \(x=-1\) E. There is a hole in its graph at \(x=-4\) F. The graph has an oblique asymptote. G. The \(x\) -axis is its horizontal asymptote. H. The \(y\) -axis is its vertical asymptote. (Column I) $$f(x)=\frac{x^{2}+3 x+4}{x-5}$$

Evaluate each expression. Do not use a calculator. $$(\sqrt[3]{-27})^{2}$$

Provide a short answer to each question. Do not use a calculator. Is \(f(x)=\frac{1}{x}\) an even or odd function? What symmetry does its graph exhibit?

Match the rational function in Column I with the appropriate description in Column II. Choices in Column II can be used only once. Do not use a calculator. (Column II) A. The \(x\) -intercept is \((-3,0)\) B. The \(y\) -intercept is \((0,5)\) C. The horizontal asymptote is \(y=4\) D. The vertical asymptote is \(x=-1\) E. There is a hole in its graph at \(x=-4\) F. The graph has an oblique asymptote. G. The \(x\) -axis is its horizontal asymptote. H. The \(y\) -axis is its vertical asymptote. (Column I) $$f(x)=\frac{x+3}{x-6}$$