Answer to Question #268539 in Algebra for Jasmine

Question

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,

Answer 1

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:

$2x^2+7x-4=0$

$D=49+32=81$

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

$x_2=(-7-9)/4=-4$

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

Horizontal asymptotes$f(x)=3x^2/2x^2=3/2$

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

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

$D=64+36=100$

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

$x_2=(8-10)/6=-1/3$

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

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