Asymptotic Behavior of Logarithmic Functions

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5 Questions

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 $y = 0$.

What is the intercept(s) of the function $f(x) = x^3$?

$(0, 0)$

Which of the following represents the domain and range of $f(x) = \sqrt{x}$?

$x \geq 0$, $y \geq 0$

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: $(0, 0)$

$y = |x|$

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?

The domain of $g(x)$ is $x \geq 5$, the y-intercept is $(0, 2)$, and the x-intercept is $(5, 0)$.

Test your knowledge of functions and graphs with this quiz! Determine the asymptotic behavior of the function f(x) = log x and choose the best statement from the options provided.

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