AP Calc Exam Study Guide

What is the result of raising a power to a power according to the exponent rules?

• A) a^(m+n)

• B) a^(m-n)

• C) a^(mn)

• D) a^(m/n)

According to the log rules, what is log(a) - log(b) equivalent to?

• A) log(a/b)

• B) log(a*b)

• C) log(a^b)

• D) log(b/a)

What is the base of natural logs (ln)?

• A) e

• B) 10

• C) 2

• D) 1

For the function f(x) = a * b^x, if b > 1, in which quadrant does the graph always pass through?

• A) Quadrant I

• B) Quadrant II

• C) Quadrant III

• D) Quadrant IV

What is the domain of the logarithmic function f(x) = log (x)?

• A) x > 0

• B) x < 0

• C) x ≥ 0

• D) All real numbers

Which of the following is a correct transformation for a vertical shift up of the function f(x)?

• A) f(x) + a

• B) f(x - a)

• C) f(x) / a

• D) f(x) * a

What is the correct simplification of the radical expression √(a^2 * b)?

• A) a * √b

• B) b * √a

• C) a^2 * b

• D) √a * √b

According to the properties of logs, what is log 1 equal to?

• A) 1

• B) 0

• C) b

• D) Undefined

What is the range of the exponential function f(x) = a * b^x when b > 1?

• A) (0, ∞)

• B) (-∞, 0)

• C) (-∞, ∞)

• D) (0, a)

What is the asymptote of the logarithmic function f(x) = log x?

• A) x-axis, y = 0

• B) y-axis, x = 0

• C) x = 1

• D) y = 1