Answer to Question #268539 in Algebra for Jasmine

Question #268539

From the function, f(x) = (3x ^ 2 - 8x - 3) / (2x ^ 2 + 7x - 4) ,




a. Construct table of values




b. Find the following:




vertical and horizontal asymptotes




x - ir intercepts or zeroes upstingit)




y- intercept,

1
Expert's answer
2021-11-23T15:12:23-0500

X=0 f(x)=3/4

X=1 f(x)=-8/5

X=-1 f(x)=-8/9

X=2 f(x)=-7/18


b. vertical asymptotes:

2x2+7x4=02x^2+7x-4=0

D=49+32=81D=49+32=81

x1=(7+9)/4=1/2x_1=(-7+9)/4=1/2

x2=(79)/4=4x_2=(-7-9)/4=-4

Vertical asymptotes are x=1/2, x=-4


Horizontal asymptotesf(x)=3x2/2x2=3/2f(x)=3x^2/2x^2=3/2


Y-interceptiins: X=0, f(x)=3/4

X-interceptions: f(x)=0, 3x28x3=03x^2-8x-3=0

D=64+36=100D=64+36=100

x1=(8+10)/6=3x_1=(8+10)/6=3

x2=(810)/6=1/3x_2=(8-10)/6=-1/3

X-interceptions: x=3, f(x)=0

x=-1/3, f(x)=0


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