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Score on last attempt: 1.7 out of 3 Score in gradebook: 1.7 out of 3 In the following questions, determine the behavior of $h(x) = \frac{4x^3 + 7x}{-x^3 + 7x}$. If a limit does not exist or the function is undefined, write DNE. a. For what value(s) of $x$ is $h(x)$ undefined? x = Preview b. For what value(s) of $x$ does $h(x)$ have a vertical asymptote? x = -\sqrt{7}, \sqrt{7} Preview c. For what value(s) of $x$ does $h(x)$ have a hole? x = Preview d. $\lim_{x \to 0} h(x) = 1$ Preview e. $\lim_{x \to \infty} h(x) = -4$ Preview f. $\lim_{x \to -\infty} h(x) = -4$ Preview g. $h(0) = \text{DNE}$ Preview h. Based on your work above, on what interval(s) is $h(x)$ continuous? $(-\infty, \infty)$ Preview $(-\infty, \infty) = (-\infty, \infty)$. Write your answer in interval notation. If you include multiple intervals, use u to denote union.

          Score on last attempt: 1.7 out of 3
Score in gradebook: 1.7 out of 3
In the following questions, determine the behavior of $h(x) = \frac{4x^3 + 7x}{-x^3 + 7x}$.
If a limit does not exist or the function is undefined, write DNE.
a. For what value(s) of $x$ is $h(x)$ undefined?
x = 
Preview
b. For what value(s) of $x$ does $h(x)$ have a vertical asymptote?
x = -\sqrt{7}, \sqrt{7}
Preview
c. For what value(s) of $x$ does $h(x)$ have a hole?
x = 
Preview
d. $\lim_{x \to 0} h(x) = 1$
Preview
e. $\lim_{x \to \infty} h(x) = -4$
Preview
f. $\lim_{x \to -\infty} h(x) = -4$
Preview
g. $h(0) = \text{DNE}$ 
Preview
h. Based on your work above, on what interval(s) is $h(x)$ continuous? $(-\infty, \infty)$
Preview $(-\infty, \infty) = (-\infty, \infty)$.
Write your answer in interval notation. If you include multiple intervals, use u to denote union.

Score on last attempt: 1.7 out of 3
Score in gradebook: 1.7 out of 3
In the following questions, determine the behavior of h(x) = (4x^3 + 7x)/(-x^3 + 7x).
If a limit does not exist or the function is undefined, write DNE.
a. For what value(s) of x is h(x) undefined?
x =
Preview
b. For what value(s) of x does h(x) have a vertical asymptote?
x = -√(7), √(7)
Preview
c. For what value(s) of x does h(x) have a hole?
x =
Preview
d. limx → 0 h(x) = 1
Preview
e. limx →∞ h(x) = -4
Preview
f. limx → -∞ h(x) = -4
Preview
g. h(0) = DNE
Preview
h. Based on your work above, on what interval(s) is h(x) continuous? (-∞, ∞)
Preview (-∞, ∞) = (-∞, ∞).
Write your answer in interval notation. If you include multiple intervals, use u to denote union.

Added by Sarah B.

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