PRE CALCULUS Advanced Topics 5 — Questions and Answers
Question 1: What is the solution set of the inequality |2x − 4| < 6?
- −1 < x < 5 (Correct answer)
- x < −1 or x > 5
- x > 5
- −5 < x < 1
Correct answer: −1 < x < 5
|2x−4|<6 gives −6<2x−4<6, so −2<2x<10, meaning −1<x<5.
Question 2: What is the horizontal asymptote of f(x) = (3x² + 1)/(x² − 4)?
- y = 3 (Correct answer)
- y = 0
- y = −1/4
- y = 1
Correct answer: y = 3
When numerator and denominator have the same degree, the horizontal asymptote is the ratio of leading coefficients: 3/1 = 3.
Question 3: Which binomial expansion term gives x³y² in (x + y)⁵?
- 10x³y² (Correct answer)
- 5x³y²
- 20x³y²
- x³y²
Correct answer: 10x³y²
The term is C(5,2)x³y² = 10x³y², using the binomial theorem with k=2.
Question 4: What type of discontinuity occurs at x = 2 in f(x) = (x²−4)/(x−2)?
- Removable discontinuity (Correct answer)
- Jump discontinuity
- Infinite discontinuity
- No discontinuity
Correct answer: Removable discontinuity
The factor (x−2) cancels, leaving f(x)=x+2 with a hole at x=2, making it a removable discontinuity.
Question 5: Which formula converts from radians to degrees?
- Multiply by 180/π (Correct answer)
- Multiply by π/180
- Multiply by 2π
- Divide by 2π
Correct answer: Multiply by 180/π
To convert radians to degrees, multiply by 180/π.
Question 6: What is the vertex of the parabola y = 2(x − 3)² + 5?
- (3, 5) (Correct answer)
- (−3, 5)
- (3, −5)
- (−3, −5)
Correct answer: (3, 5)
In vertex form y = a(x−h)²+k, the vertex is (h, k) = (3, 5).
Question 7: If f(x) = log₃(x), what is f(81)?
- 4 (Correct answer)
- 3
- 9
- 27
Correct answer: 4
log₃(81) = log₃(3⁴) = 4.
PRE CALCULUS Advanced Topics 5
What is the solution set of the inequality |2x − 4| < 6?