Match the function $f ( x ) = \frac { 4 x + 3 } { 5 x + 6 }$ , use a graphing utility to complete the table and estimate the limit as x approaches infinity. $\begin{array}{|c|c|c|c|c|c|c|c|}
\hline x & 10^{0} & 10^{1} & 10^{2} & 10^{3} & 10^{4} & 10^{5} & 10^{6} \
\hline f(x) & & & & & & & \
\hline
\end{array}$

A) $0.8000$
B) $1.8000$
C) $1.2500$
D) $2.2500$
E) $0.2500$

Question

Match the function $f ( x ) = \frac { 4 x + 3 } { 5 x + 6 }$ , use a graphing utility to complete the table and estimate the limit as x approaches infinity. $\begin{array}{|c|c|c|c|c|c|c|c|}
\hline x & 10^{0} & 10^{1} & 10^{2} & 10^{3} & 10^{4} & 10^{5} & 10^{6} \
\hline f(x) & & & & & & & \
\hline
\end{array}$

A) $0.8000$
B) $1.8000$
C) $1.2500$
D) $2.2500$
E) $0.2500$

Quizplus · Accepted Answer

To estimate the limit of $f(x) = \frac{4x + 3}{5x + 6}$ as $x$ approaches infinity, we can divide the numerator and the denominator by the highest power of $x$ in the denominator, which is $x$. This simplifies the function to $\frac{4 + \frac{3}{x}}{5 + \frac{6}{x}}$. As $x$ approaches infinity, the terms $\frac{3}{x}$ and $\frac{6}{x}$ approach 0, leaving us with $\frac{4}{5}$ or $0.8000$.

Match the Function f(x)=4x+35x+6f ( x ) = \frac { 4 x + 3 } { 5 x + 6 }f(x)=5x+64x+3​

Match the Function $f ( x ) = \frac { 4 x + 3 } { 5 x + 6 }$