Provide an appropriate response.
-Graph the functions $f ( x ) = \frac { x } { 2 }$ and $g ( x ) = 1 + \frac { 4 } { x }$ together to identify the values of $x$ for which $\frac { x } { 2 } 1 + \frac { 4 } { x }$. Confirm your findings algebraically.
A) $( - \infty , - 2 ) \cup ( 0,4 )$
B) $( - 2,4 )$
C) $( 4 , \infty )$
D) $( - 2,0 ) \cup ( 4 , \infty )$

Question

Provide an appropriate response.
-Graph the functions $f ( x ) = \frac { x } { 2 }$ and $g ( x ) = 1 + \frac { 4 } { x }$ together to identify the values of $x$ for which $\frac { x } { 2 } > 1 + \frac { 4 } { x }$. Confirm your findings algebraically.
A) $( - \infty , - 2 ) \cup ( 0,4 )$
B) $( - 2,4 )$
C) $( 4 , \infty )$
D) $( - 2,0 ) \cup ( 4 , \infty )$

Quizplus · Accepted Answer

To graph the functions, we can create a table of values and plot points.

For $f(x)=\frac{x}{2}$:

| x   | f(x)  |
| --- | ---   |
| -4  | -2    |
| -2  | -1    |
| 0   | 0     |
| 2   | 1     |
| 4   | 2     |

For $g(x)=1+\frac{4}{x}$:

| x   | g(x)   |
| --- | ---    |
| -4  | 2      |
| -2  | -1     |
| -1  | -3     |
| 1   | 5      |
| 2   | 3      |

Plotting these points, we get the following graph:

![graph](https://i.imgur.com/vi5CKnG.png)

We want to find the values of $x$ for which $\frac{x}{2}>1+\frac{4}{x}$:

\begin{align*}
\frac{x}{2}&>1+\frac{4}{x}\
\frac{x^2}{2}&>x+4\
x^2&>2x+8\
x^2-2x-8&>0\
(x-4)(x+2)&>0
\end{align*}

So the solutions are $x<-2$ or $x>4$. Therefore, the answer is D, $(-2,0)\cup(4,\infty)$.

Provide an Appropriate Response f(x)=x2f ( x ) = \frac { x } { 2 }f(x)=2x​

Provide an Appropriate Response $f ( x ) = \frac { x } { 2 }$