Write the word or phrase that best completes each statement or answers the question.
Provide the missing information.
-Given $f ( x ) = \frac { 2 x ^ { 3 } + 7 } { 5 x ^ { 3 } }$, the graph of $f$ will behave like the graph of which of the following functions for large values of $| x |$ ?
A) $y = \frac { 2 } { 5 x }$
B) $y = \frac { 2 x } { 5 }$
C) $y = \frac { 2 } { 5 }$
D) $\mathrm { y } = \frac { 2 } { 5 } x ^ { 3 }$

Question

Quizplus · Accepted Answer

For large values of $|x|$, the behavior of the function $f(x) = \frac{2x^3 + 7}{5x^3}$ is dominated by the terms with the highest power of $x$ in both the numerator and the denominator. Thus, the function behaves like $y = \frac{2}{5}$, as the $x^3$ terms cancel out.

Write the Word or Phrase That Best Completes Each Statement f(x)=2x3+75x3f ( x ) = \frac { 2 x ^ { 3 } + 7 } { 5 x ^ { 3 } }f(x)=5x32x3+7​

Write the Word or Phrase That Best Completes Each Statement $f ( x ) = \frac { 2 x ^ { 3 } + 7 } { 5 x ^ { 3 } }$