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Sketch the graphs of each of the following functions showing all steps on the same set of axe

Sketch The Graphs Of Each Of The Following Functions Showing All Steps On The Same Set Of Axe class=

Sagot :

Part D

we have the function

[tex]\begin{gathered} y=\frac{4}{-(x+1)}+3=\frac{4-3(x+1)}{-(x+1)}=\frac{4-3x-3}{-(x+1)}=\frac{1-3x}{-(x+1)}=\frac{3x-1}{x+1} \\ \\ y=\frac{3x-1}{x+1} \end{gathered}[/tex]

In this rational function

Remember that

The denominator cannot be equal to zero

so

The value of x cannot be equal to x=-1

At x=-1 there is a vertical asymptote

Find out a horizontal asymptote

Degree on Top is Equal to the Bottom

so

the horizontal asymptote is at y=3/1=3

Find out the intercepts

y-intercept (value of y when the value of x=0)

For x=0

[tex]y=\frac{3(0)-1}{0+1}=-1[/tex]

The y-intercept is (0,-1)

Find out the x-intercept (value of x when the value of y=0)

For y=0

[tex]\begin{gathered} 0=\frac{3x-1}{x+1} \\ \\ 3x-1=0 \\ 3x=1 \\ x=\frac{1}{3} \end{gathered}[/tex]

The x-intercept is (0.33,0)

With the given information

Graph the function

using a graphing tool

see the figure below

View image WendellG69484
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