Question

NO LINKS!! Graph the following rational functions. Please show all of the work​

Answer 1

To graph rational functions:

• Find any asymptotes (draw them as dotted lines, unless they are x and y axis)
• Find any x-intercept(s) and y-intercept
• Find the values of y for different values of x
• Plot the points and connect them with a smooth curve

Part (a)

`\textsf{Asymptote} \implies (x+3)^2=0 \implies x=-3`

`(x+3)^2\geq 0 \implies f(x) > 0 \implies \textsf{asymptote}:y=0`

`\textsf{y-intercept}\implies (1)/((0+3)^2)=(1)/(9) \implies \left(0,(1)/(9)\right)`

Part (b)

`\textsf{Factor denominator} \implies x^2+2x-3=(x-1)(x+3)`

`\textsf{Asymptote} \implies x-1=0 \implies x=1`

`\textsf{Asymptote} \implies x+3=0 \implies x=-3`

`\textsf{x-intercept} \implies x+1=0 \implies x=-1 \implies (-1,0)`

`\textsf{y-intercept}\implies (0+1)/(0^2+2(0)-3)=-(1)/(3) \implies \left(0,-(1)/(3)\right)`

Part (c)

`\textsf{Asymptote} \implies x-2=0 \implies x=2`

`\textsf{x-intercepts} \implies x^2-9=0 \implies x=\pm 3 \implies (-3,0)\:(3,0)`

`\textsf{y-intercept}\implies (0^2-9)/(0-2)=(-9)/(-2)=4.5 \implies (0,4.5)`