PRE CALCULUS Exponential and Logarithmic Functions

Question 1

Which of the following is the general form of an exponential function?

Accepted Answer

f(x) = a·b^x where b > 0, b ≠ 1

Answer

An exponential function has the form f(x) = a·b^x where b is a positive base not equal to 1 and x is the exponent.

Question 2

What is the y-intercept of the function f(x) = 3·2^x?

Accepted Answer

3

Answer

At the y-intercept, x = 0, so f(0) = 3·2^0 = 3·1 = 3.

Question 3

Which statement describes the end behavior of f(x) = (1/2)^x as x → ∞?

Accepted Answer

f(x) → 0

Answer

Since the base 1/2 is between 0 and 1, repeated multiplication makes (1/2)^x approach 0 as x increases.

Question 4

What is the value of e^0?

Accepted Answer

1

Answer

Any nonzero number raised to the power of 0 equals 1, so e^0 = 1.

Question 5

The exponential function f(x) = 5^x is a one-to-one function. What does this imply?

Accepted Answer

Its inverse is also a function

Answer

Because f(x) = 5^x is one-to-one (passes the horizontal line test), its inverse (the logarithm) is also a valid function.

PRE CALCULUS Practice Test