PRE CALCULUS Advanced Topics 5

Question 1

What is the solution set of the inequality |2x − 4| < 6?

Accepted Answer

−1 < x < 5

Answer

|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)?

Accepted Answer

y = 3

Answer

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?

Accepted Answer

10x³y²

Answer

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)?

Accepted Answer

Removable discontinuity

Answer

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?

Accepted Answer

Multiply by 180/π

Answer

To convert radians to degrees, multiply by 180/π.

PRE CALCULUS Practice Test