Functions and Logarithms Assessment

The video tutorial covers a range of mathematical concepts, starting with an introduction and overview of quiz questions. It delves into domain and range, graph analysis, polynomial division, and synthetic division. The tutorial also explains logarithms, exponent rules, limits, and asymptotes, providing a comprehensive review of these topics.

What is the result of factoring the quadratic expression x^2 + x - 6?

• (x - 1)(x + 6)

• (x + 1)(x - 6)

• (x - 2)(x + 3)

• (x + 2)(x - 3)

Which of the following is NOT a valid domain for the function f(x) = sqrt(x - 5)?

• x ≥ 5

• x > 5

• x = 5

• x ≤ 5

What is the range of a parabola with vertex at (3, -2) that opens upwards?

• y < -2

• y > -2

• y ≤ -2

• y ≥ -2

When performing synthetic division, what is the divisor if the polynomial is divided by x - 3?

• 3

• x + 3

• -3

• x - 3

What is the horizontal asymptote of the function f(x) = (3x^2 + 2x + 1)/(x^2 + 4)?

• y = 2

• y = 1

• y = 0

• y = 3

Which of the following is the correct expression for log base 2 of 8?

• 3

• 1

• 2

• 4

What is the value of log base 10 of 1000?

• 5

• 4

• 3

• 2

If f(x) = log base 3 of x, what is f(27)?

• 0

• 1

• 3

• 2

What is the inverse of the function f(x) = log base 5 of x?

• log base x of 5

• x^5

• 1/5^x

• 5^x

Which of the following is the correct simplification of ln(e^3)?

• 0

• 1

• e^3

• 3