Academic Calculus - Unit 1 Test Review

• All real numbers, (-∞,∞)

• All real numbers except x = 1

• All real numbers except x = ±1

• All real numbers except x = 3/2

Answer explanation

Remember in a rational function, the denominator is not allowed to equal to zero.

• all real numbers (-∞,∞)

• x ≥ -3 except x = 3 and x = -2

• all real numbers except x = -5 and x = 1

• x ≥ -3 except x = -2 and x = -3

• x = 2, removable discontinuity

• x = 2, non-removable discontinuity

• x = 4, removable discontinuity

• x = 4, non-removable discontinuity

• x = -2 and x = 2, both removable discontinuities

• x = -2 and x = 2, both non-removable discontinuities

• x = -2 and x = 2, one removable and one non-removable

• x = -3 and x = 2, both removable discontinuities

• domain: all real numbers
  range: all real numbers

• domain: x ≥ 3
  range: y ≥ -2

• domain: all real numbers
  range: y ≤ -2

• domain: x ≥ 3
  range: y ≤ -2

• domain: all real numbers

  range: y ≤ 0

• domain: x ≤ 2

  range: y ≥ 0

• domain: x ≤ 2

  range: all real numbers

• domain: all real numbers

  range: y ≥ 0

Given the absolute value parent function, select the equation that would produce the following transformations: shifted up three and right two. Then vertically compressed by a factor of one-half.

Given the absolute value parent function, select the equation that would produce the following transformations: a reflection over the x-axis, then shifted four units down and one unit to the left. Then vertically compressed by a factor of one-third.