1) f(x) = (-3x + 12)/(x² - 3x - 4)
a) Vertical Asymptotes: x = -1, x = 4
b) Horizontal Asymptote: y = 0
c) Holes: None
d) X-intercept(s): (4, 0)
e) Y-intercept(s): (0, -3)
f) Domain: {x | x ≠ -1, x ≠ 4}
g) Range: All real numbers except y = 0 and the value at the hole if it existed (but there is none), so range is all real numbers.
2) f(x) = (x² - 3x)/(2x² + 2x - 12)
a) Vertical Asymptotes: x = -3, x = 2
b) Horizontal Asymptote: y = 1/2
c) Holes: None
d) X-intercept(s): (0, 0), (3, 0)
e) Y-intercept(s): (0, 0)
f) Domain: {x | x ≠ -3, x ≠ 2}
g) Range: All real numbers except y = 1/2
3) f(x) = (-2x² + 4x + 16)/(x² - 5x + 4)
a) Vertical Asymptotes: x = 1, x = 4
b) Horizontal Asymptote: y = -2
c) Holes: None
d) X-intercept(s): (-2, 0), (4, 0) — but x=4 is a vertical asymptote, so only (-2, 0) is valid
e) Y-intercept(s): (0, 4)
f) Domain: {x | x ≠ 1, x ≠ 4}
g) Range: All real numbers except y = -2
4) f(x) = (x² + 7x + 12)/(-2x² - 2x + 12)
a) Vertical Asymptotes: x = -3, x = 2
b) Horizontal Asymptote: y = -1/2
c) Holes: None
d) X-intercept(s): (-4, 0), (-3, 0) — but x=-3 is a vertical asymptote, so only (-4, 0) is valid
e) Y-intercept(s): (0, 1)
f) Domain: {x | x ≠ -3, x ≠ 2}
g) Range: All real numbers except y = -1/2
Parent Tip: Review the logic above to help your child master the concept of asymptote worksheet.
