Exponential/Logarithmic Functions

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 general form of a logarithmic function?

Back

The general form of a logarithmic function is y = log_b(x), where 'b' is the base of the logarithm and 'x' is the argument.

Tags

CCSS.HSF-IF.C.7E

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 does it mean for a function to exhibit exponential growth?

Back

Exponential growth occurs when a quantity increases at a rate proportional to its current value, typically represented by a function of the form y = a * b^x where b > 1.

Tags

CCSS.HSF-IF.C.8B

Front

What does it mean for a function to exhibit exponential decay?

Back

Exponential decay occurs when a quantity decreases at a rate proportional to its current value, typically represented by a function of the form y = a * b^x where 0 < b < 1.

Tags

CCSS.HSF-IF.C.8B

Front

How do you find the y-intercept of an exponential function?

Back

The y-intercept of an exponential function y = a * b^x is found by evaluating the function at x = 0, which gives y = a.

Tags

CCSS.HSF-IF.C.7E

Front

What is the domain of the function y = 2^x?

Back

The domain of the function y = 2^x is all real numbers, expressed as (-∞, ∞).

Front

What is the range of the function y = 2^x?

Back

The range of the function y = 2^x is all positive real numbers, expressed as (0, ∞).

Front

How do you evaluate log_5(25)?

Back

To evaluate log_5(25), you determine what power you raise 5 to in order to get 25. Since 5^2 = 25, log_5(25) = 2.

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(x), 'b' is the base.

Tags

CCSS.HSF.BF.B.5