Pre-calculus Practice Quiz 1.7-1.11

For the function f(x) = (x+1)/(2x+5): State the domain of the following rational function by using interval notation.

• The domain is all real numbers except x = -5/2, so (-∞, -5/2) ∪ (-5/2, ∞).

• The domain is all real numbers except x = 0, so (-∞, 0) ∪ (0, ∞).

• The domain is all real numbers except x = 2, so (-∞, 2) ∪ (2, ∞).

• The domain is all real numbers except x = -1, so (-∞, -1) ∪ (-1, ∞).

For the function f(x) = (x+1)/(2x+5): Find the horizontal or slant asymptote.

• The horizontal asymptote is y = 1/2.

• The horizontal asymptote is y = 2.

• The slant asymptote is y = x/2.

• There is no horizontal or slant asymptote.

For the function f(x) = (x+1)/(2x+5): Use your HA or SA to determine the end behavior of the function.

• As x approaches ±∞, f(x) approaches 1/2.

• As x approaches ±∞, f(x) approaches 2.

• As x approaches ±∞, f(x) approaches 0.

• As x approaches ±∞, f(x) approaches 5.

• The domain is all real numbers since the denominator has no real roots. (-∞, ∞)

• The domain is all real numbers except x = -2. (-∞, -2) ∪ (-2, ∞)

• The domain is all real numbers except x = 0. (-∞, 0) ∪ (0, ∞)

• The domain is all real numbers except x = -5. (-∞, -5) ∪ (-5, ∞)

• The slant asymptote is y = x + 5 (from polynomial long division).

• The horizontal asymptote is y = 0.

• The slant asymptote is y = x - 2.

• The horizontal asymptote is y = 1.

• As x approaches ±∞, h(x) approaches the slant asymptote y = x + 5.

• As x approaches ±∞, h(x) approaches the horizontal asymptote y = 0.

• As x approaches ±∞, h(x) approaches the horizontal asymptote y = 1.

• As x approaches ±∞, h(x) approaches the slant asymptote y = x - 2.

• The domain is all real numbers except x = 6 and x = -4, so (-∞, -4) ∪ (-4, 6) ∪ (6, ∞).

• The domain is all real numbers except x = 4 and x = -6, so (-∞, -6) ∪ (-6, 4) ∪ (4, ∞).

• The domain is all real numbers except x = 2 and x = -12, so (-∞, -12) ∪ (-12, 2) ∪ (2, ∞).

• The domain is all real numbers except x = 1 and x = -24, so (-∞, -24) ∪ (-24, 1) ∪ (1, ∞).

• The horizontal asymptote is y = 0.

• The horizontal asymptote is y = 4.

• The slant asymptote is y = x.

• The horizontal asymptote is y = 1.

• As x approaches ±∞, g(x) approaches 0.

• As x approaches ±∞, g(x) approaches ∞.

• As x approaches ±∞, g(x) approaches 4.

• As x approaches ±∞, g(x) approaches -1.

• (−2, 0) ∪ (2, ∞)

• (−∞, −2) ∪ (0, 2)

• (−∞, 0) ∪ (2, ∞)

• (−2, 0) ∪ (0, 2)