Asymptotic Behavior of Logarithmic Functions
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Questions and Answers

Which statement best describes the asymptotic behavior of the graph of the function $f(x) = \log x$?

  • The graph of $f(x) = \log x$ approaches and does not cross the line $y = 0$. (correct)
  • The graph of $f(x) = \log x$ has no asymptotic behavior.
  • The graph of $f(x) = \log x$ approaches and does not cross the line $x = 0$.
  • The graph of $f(x) = \log x$ approaches and crosses the line $y = 2$.
  • What is the intercept(s) of the function $f(x) = x^3$?

  • $(-1, 0)$ and $(0, 0)$
  • $(0, 0)$ (correct)
  • $(1, 0)$ and $(0, 0)$
  • $-0.5 < x < 0.5$
  • Which of the following represents the domain and range of $f(x) = \sqrt{x}$?

  • $x > 0$, $y > 0$
  • $x \geq 0$, $y > 0$
  • $x \geq 0$, $y \geq 0$ (correct)
  • $x > 0$, $y \geq 0$
  • Which of the following identifies the correct parent function and graph for the attributes shown below?\nDomain: $(-\infty, \infty)$\nRange: $[0, \infty)$\nx-intercept: $0$\ny-intercept: $0$\nReflectional symmetry across $x = 0$\nMinimum: $(0, 0)$

    <p>$y = |x|$</p> Signup and view all the answers

    The graph of $g(x) = \log_2(x - 5) + 2$ is shown on the coordinate grid. Which statement about the domain, the y-intercept, and the x-intercept is true?

    <p>The domain of $g(x)$ is $x \geq 5$, the y-intercept is $(0, 2)$, and the x-intercept is $(5, 0)$.</p> Signup and view all the answers

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