? Exercise 3.7.5 Find the horizontal and vertical intercepts of \( f(x)=\frac{(x+1)(x-4)}{(x-3)(x+7)} \). Horizontal intercepts: \( (x, y)= \) (list all, separated by commas) Vertical intercept: \( (x, y)=\square \)

To find the intercepts of the function f(x) = ((x + 1)(x - 4)) / ((x - 3)(x + 7)): 1. Horizontal intercepts (x-intercepts):  • Set the numerator equal to 0:   (x + 1)(x - 4) = 0.   Solutions: x + 1 = 0 ⟹ x = -1 , x - 4 = 0 ⟹ x = 4.  • Both x = -1 and x = 4 are acceptable provided they do not make the denominator zero (check: -1 ≠ 3, -1 ≠ -7; 4 ≠ 3, 4 ≠ -7).  • Therefore, the horizontal intercepts are: (-1, 0) and (4, 0). 2. Vertical intercept (y-intercept):  • Set x = 0:   f(0) = ((0 + 1)(0 - 4)) / ((0 - 3)(0 + 7)) = (1 * (-4)) / ((-3) * 7) = (-4) / (-21) = 4/21.  • Thus, the vertical intercept is: (0, 4/21). Final Answers: Horizontal intercepts: (-1, 0), (4, 0)  Vertical intercept: (0, 4/21)