Semester Exam ( Exponential and Logarithms Basic)

Front

What is the right end behavior of an exponential function?

Back

As x approaches positive infinity, f(x) approaches positive infinity.

Front

What is the domain and range of the exponential function?

Back

Domain: all real numbers; Range: y > -2.

Front

Determine the equation of the asymptote for the function.

Back

x = 4.

Front

What is the asymptote of the exponential function?

Back

y = 4.

Front

If you invest $400 for 5 years at an interest rate of 4.29% per year, what is the formula to calculate the amount?

Back

y = 400(1 + 0.0429)^5.

Front

Define an exponential function.

Back

A function of the form f(x) = a * b^x, where a is a constant, b is a positive real number, and x is the exponent.

Front

What is the general form of a logarithmic function?

Back

A function of the form f(x) = log_b(x), where b is the base and x is the argument.

Front

What is the relationship between exponential and logarithmic functions?

Back

They are inverses of each other; if y = b^x, then x = log_b(y).

Front

What is the base of natural logarithms?

Back

The base of natural logarithms is e, approximately equal to 2.718.

Front

What is the value of log_e(e)?

Back

1, because any logarithm of its base is equal to 1.