Summarize the graph features of the following rational function: f(x) = (x + 3) / (x - 2) a. Domain: (-∞,...

Question

14. Summarize the graph features of the following rational function:
f(x) = (x + 3) / (x - 2)
a. Domain: (-∞, 2) U (2, ∞)
Hole: none
x-intercept: (-3, 0)
y-intercept: (0, -3/2)
Vertical asymptote: x = 2
Horizontal asymptote: y = 1
b. Domain: (-∞, 2) U (2, ∞)
Hole: none
x-intercept: (3, 0)
y-intercept: (0, -3)
Vertical asymptote: x = -2
Horizontal asymptote: y = 1
c. Domain: (-∞, 2) U (2, ∞)
Hole: (2, 5)
x-intercept: (-3, 0)
y-intercept: (0, -3/2)
Vertical asymptote: x = 2
Horizontal asymptote: y = 1
d. Domain: (-∞, 3) U (3, ∞)
Hole: none
x-intercept: (-3, 0)
y-intercept: (0, 3/2)
Vertical asymptote: x = 3
Horizontal asymptote: y = 0

SnapAndSolve AI · Accepted Answer

a. Correct. The domain is (-∞, 2) U (2, ∞) because the function is undefined at x = 2. There is no hole. The x-intercept is found by setting the numerator equal to zero, giving (-3, 0). The y-intercept is found by evaluating f(0), which is (0, -3/2). The vertical asymptote is at x = 2, where the denominator is zero. The horizontal asymptote is y = 1, as the degrees of the numerator and denominator are the same, and the leading coefficients are both 1.

b. Incorrect. The x-intercept is not (3, 0), and the vertical asymptote is not x = -2.

c. Incorrect. There is no hole at (2, 5).

d. Incorrect. The domain and vertical asymptote are incorrect.

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Summarize the graph features of the following rational function: f(x) = (x + 3) / (x - 2) a. Domain: (-∞,...

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