Use a calculator to graph the rational function in the window indicated. Use the graph to (a) give the x- and y-intercepts, (b) explain why there are no vertical asymptotes, (c) give the equation of the oblique asymptote, and (d) give the domain and range.f(x) =
; [-5, 5] by [-11, 11]
A. (a) x-intercepts: (-3, 0), , (3, 0); y-intercept:
;
(b) The denominator has no real zeros because the discriminant, -17, is negative.;
(c) y = 3x + 1;
(d) The domain and range are both [0, ?).
B. (a) x-intercepts: (-4, 0), , (4, 0); y-intercept:
;
(b) The denominator has no real zeros because the discriminant, -17, is negative.;
(c) y = 3x + 6;
(d) The domain and range are both (-?, ?).
C. (a) x-intercepts: (-4, 0), ,
; y-intercept:
;
(b) The denominator has no real zeros because the discriminant, -15, is negative.;
(c) y = 3x + 0;
(d) The domain and range are both [0, ?).
D. (a) x-intercepts: (-3, 0), , (3, 0); y-intercept:
;
(b) The denominator has no real zeros because the discriminant, -15, is negative.;
(c) y = 3x + 1;
(d) The domain and range are both (-?, ?).
Answer: D
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