Graph a rational function

Question

Find the Find the x and y intercepts and all asymptotes for the following:

y = (2x+21)/(x+7)

Answer 1

For the y intercept, set x=0 and solve

y = (2(0)+21)/(0+7) = 21/7 = 3

y intercept = (0,3)

For the x intercept, set y=0 and solve

0 = (2x+21)/(x+7) Multiply both sides by (x+7)

0 = (2x+21) Subtract 21 from both sides

-21 = 2x Divide both sides by 2

x=-21/2

x intercept = (-21/2,0)

Vertical asymptote, set the denominator equal to zero and solve

x+7=0 Subtract 7 from bother sides

x=-7

Horizontal asymptote, looks at the exponents of the leading terms in the numerator and denominator. They are equal. So the HA equals the coefficients

y=2/1

y=2

Answer 2

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