Question

Which graph represents the function f(x)=4/x

Answer 1

Answer with explanation:

The given function is:

   $f(x)=\frac{4}{x}$

→Domain and Range of the function is ,all real number excluding 0, which can be written as, x ∈ R→{0} and y∈ R→{0}.

So, if we replace , f(x) by, y ,the equation of function will become

 x y = 4,which is rectangular Hyperbola.

→Horizontal Asymptote

$y=\lim_{x \to \infty} \frac{4}{x}=0$

→Vertical Asymptote

$x=\lim_{y \to \infty}\frac{4}{y}=0$

Answer 2

Answer:

The graph of given function is shown below.

Step-by-step explanation:

The given function is

$f(x)=\frac{4}{x}$

We need top find the graph of given rational function.

First find the key features of the given function.

1. Vertical asymptote: Equate denominator equal to 0.

$x=0$

The vertical asymptote is x=0.

2. Horizontal asymptote: Find the $y=lim_{x\rightarrow \infty}f(x)$ to find the horizontal asymptote.

$y=lim_{x\rightarrow \infty}f(x)=lim_{x\rightarrow \infty}\frac{4}{x}$

$y=\frac{4}{ \infty}$

$y=0$

The horizontal asymptote is y=0.

3. The graph has vertical asymptote is x=0 and horizontal asymptote is y=0, therefore the graph has no x- and y-intercepts.

4. End behavior:

$f(x)\rightarrow 0\text{ as }x\rightarrow -\infty$

$f(x)\rightarrow -\infty\text{ as }x\rightarrow 0^-$

$f(x)\rightarrow \infty\text{ as }x\rightarrow 0^+$

$f(x)\rightarrow =\text{ as }x\rightarrow \infty$

5. Table of value:

The table of values is

x               f(x)

-2              -2

-1               -4

1                 4

2                2

Plot these ordered pairs on a coordinate and connect these points by free hand curve using the key features.