# The Graph of a Rational Function 4.3 - Math 121 Section 4.3...

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Math 121 – Section 4.3 Solutions7.R(x) =x+ 1x(x+ 4)the domain is allxexceptx= 0,-4; there is noy-interceptthex-intercept is atx=-1the vertical asymptotes arex= 0 andx=-4the horizontal asymptote isy= 0table:Interval(-∞,-4)(-4,-1)(-1,0)(0,)Number Chosen-5-2-121Value ofRR(-5) =-45R(-2) =14R(-12) =-27R(1) =25Location of graphbelowx-axisabovex-axisbelowx-axisabovex-axisPoint on graph(-5,-45)(-2,14)(-12,-27)(1,25)xy0112233-1-1-2-2-3-3-4-5-6-7(-5,-45)(-2,14)(-1,0)(-12,-27)(-1,25)9.R(x) =3x+ 32x+ 4=3(x+ 1)2(x+ 2)the domain is allxexceptx=-2; they-intercept is atR(0) =34thex-intercept is atx=-1the vertical asymptote isx=-2the horizontal asymptote isy=321
table:Interval(-∞,-2)(-2,-1)(-1,)Number Chosen-3-320Value ofRR(-3) = 3R(-32) =-32R(0) =34Location of graphabovex-axisbelowx-axisabovex-axisPoint on graph(-3,3)(-32,-32)(0,34)xy01122345-1-1-2-2-3-3-4-5(-3,3)(-32,-32)(-1,0)(0,34)12.R(x) =6x2-x-6=6(x-3)(x+ 2)the domain is allxexceptx=-2,

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