Question

21. 8 pts For the function g(x) = = 4x2-1 214x A. Find the horizontal asymptote. B. Find the vertical asymptote(s). 0. Find the x intercept(s). D. Solve g(x) <0. Use interval notation. E. Graph g(x)

Answer 1

62-) gobe but droitola et 24442 svoT g(x) = ing coeffrent & Horizontal asymptote: - denominator's degree > numerator's degree, then Horizonte asymptore is the x-asis, 43001 by numerator's degree - it denominator's degree, the asymptot is a sthant asymptote of the form: y = math. if degree's are equal, the asymptote is Y = numerator's leading coefficient 0 denominator's leading coeffient numerator's degree > 1+ denominator's degree, there horizontal approptole. P or Here numarator degree -denominator degree=2.. y=4 => Horizonatal asymptote is (y=4]. B vertical Asymptole: These are the undefined points, also known as zeros of the denominator of the simplified function. Xrt4x=0 x(x+4)=0 =) ao, xty=0 e) x=-4. a vertical asymptotes are X=-4, x=0. ©x intercepts. x-intercept is a point on the graph where yo take nomerator equals to o and some for x a - 4x01 = 0 =) 4x=) =) xr = Y = x= 1/4 - X=V2 SHOT ON REDMI 7 ALDITAL CAMERA

To verify the solutions. (Find undefined points) Take denominato equat and compare tozean. = x +48=0 = x (x+4)=0 = x=0, x=-4. ro combine undefined points with solution. ily way, 9th a = /2 x=-/. X-intercept points (1/10), (-Y210). 6 since we already found the interver is of a =) 2=0,&x=-4. we can write it as xc-4.or-ucxlo 8 xx interval notation is (+20,-4) 4 (416) (0,0). since, if you put x=0&x=-4 in 9(a) we will get this function as undefined, so se @ grophi e Range = (0,2). 3 I cho - 2 25 - 2.5 2 5 to

interval notations x=0,x=-4

use these x values in g(x).

then for x=0, g(x)=-1/0 and x=-4 then g(x)=63/0 which is undefined