Question

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

Answer 1

Part D

we have the function

$\begin{gathered} y=\frac{4}{-(x+1)}+3=\frac{4-3(x+1)}{-(x+1)}=\frac{4-3x-3}{-(x+1)}=\frac{1-3x}{-(x+1)}=\frac{3x-1}{x+1} \\ \\ y=\frac{3x-1}{x+1} \end{gathered}$

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

$y=\frac{3(0)-1}{0+1}=-1$

The y-intercept is (0,-1)

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

For y=0

$\begin{gathered} 0=\frac{3x-1}{x+1} \\ \\ 3x-1=0 \\ 3x=1 \\ x=\frac{1}{3} \end{gathered}$

The x-intercept is (0.33,0)

With the given information

Graph the function

using a graphing tool

see the figure below