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=(4)/(-(x+1))+3=(4-3(x+1))/(-(x+1))=(4-3x-3)/(-(x+1))=(1-3x)/(-(x+1))=(3x-1)/(x+1) \\ \\ y=(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=(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=(3x-1)/(x+1) \\ \\ 3x-1=0 \\ 3x=1 \\ x=(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