Exponential & Logarithmic Expressions/graphs

Front

What is an exponential function?

Back

An exponential function is a mathematical function of the form y = a * b^x, where a is a constant, b is the base (a positive real number), and x is the exponent.

Front

What is the base of a logarithm?

Back

The base of a logarithm is the number that is raised to a power to obtain a given number. For example, in log_b(a) = c, b is the base.

Tags

CCSS.HSF.BF.B.5

Front

What is the relationship between exponential and logarithmic functions?

Back

Exponential functions and logarithmic functions are inverses of each other. If y = b^x, then x = log_b(y).

Tags

CCSS.HSF.BF.B.5

Front

What is the y-intercept of an exponential function?

Back

The y-intercept of an exponential function y = a * b^x is the point where x = 0, which is (0, a).

Tags

CCSS.HSF-IF.C.7E

Front

What is an asymptote in the context of exponential functions?

Back

An asymptote is a line that a graph approaches but never touches. For the function y = b^x, the horizontal asymptote is y = 0.

Tags

CCSS.HSF-IF.C.7E

Front

How do you convert a logarithmic expression to exponential form?

Back

To convert log_b(a) = c to exponential form, rewrite it as b^c = a.

Tags

CCSS.HSF.BF.B.5

Front

What is the value of log_10(100)?

Back

log_10(100) = 2, because 10^2 = 100.

Tags

CCSS.HSF.BF.B.5

Front

What is the value of log_2(8)?

Back

log_2(8) = 3, because 2^3 = 8.

Tags

CCSS.HSF.BF.B.5

Front

What is the domain of an exponential function?

Back

The domain of an exponential function is all real numbers, (-∞, ∞).

Front

What is the range of an exponential function?

Back

The range of an exponential function y = a * b^x (where a > 0) is (0, ∞).