Use the seven step strategy to graph the rational function f

Use the seven step strategy to graph the rational function, f(x) = x + 2/x^2 + x - 6. Show work for the first. Solve the equation 2Cos^2x + Sin x = 1 for all x such that 0 lessthanorequalto x

Solution

f(x) = (x+2)/(x²+x - 6)

step 1.     First we have to check for the symmetry

   And f(-x)= (-x+2)/((-x)²+(-x)-6) = (-x +2)/(x² -x-6)

It is neither symmetric to y axis nor to origin

step 2. In next step we have to find the vertical asymptote. And to find the vertical asymptote,we have to set the denominator to zero

x²+x -6=0

(x+3)(x-2)=0

x=-3,2Therefore the vertical asymptotes are x=-3 and x=2

step 3. In this step we have to find the horizontal asymptote.

             In the given expression the degree of numerator is 1 less than the degree of the denominator. And in such case the horizontal asymptote is y=0

step 4. In this step we have to find the x intercept and to find the x intercept we have to plug f(x)=0

(x+2)/(x²+x-6) =0

x+2=0 x=-2

Therefore the xintercept is (-2,0)

step 5. In this step we have to find the y intercept and to find the y intercept we have to plug x=0

f(x)=(0+2)/(0²+0-6)=-1/3

Therefore the y intercept is (0,-1/3)

step 6. In this step we need some points. And our points are

(-2,0),(-1,-0.167),(0,-.33),(-4,-0.33),(4,.43)