PRE CALCULUS Advanced Topics 3

Question 1

If the discriminant of a quadratic equation is negative, how many real solutions does it have?

Accepted Answer

No real solutions

Answer

A negative discriminant (b²−4ac < 0) means the roots are complex, so there are no real solutions.

Question 2

What is the magnitude of the vector v = ⟨−3, 4⟩?

Accepted Answer

5

Answer

|v| = √((-3)²+4²) = √(9+16) = √25 = 5.

Question 3

Which identity is equivalent to sin²x + cos²x?

Accepted Answer

1

Answer

The Pythagorean identity states sin²x + cos²x = 1 for all x.

Question 4

What is the inverse function of f(x) = 2x − 6?

Accepted Answer

f⁻¹(x) = (x+6)/2

Answer

Replace f(x) with y, swap x and y to get x=2y−6, then solve: y=(x+6)/2.

Question 5

Which of the following represents a one-to-one function?

Accepted Answer

f(x) = x³

Answer

f(x)=x³ is strictly increasing and passes the horizontal line test, so it is one-to-one.

PRE CALCULUS Practice Test