Domain of Exponential Functions

Gabriella is determining the domain of an exponential function. The video explains that the domain refers to the valid inputs, which are the X values in a function. It highlights that both negative and positive numbers, including decimals and fractions, are valid inputs. Therefore, the domain should be all real numbers, as integers alone are not sufficient. The video emphasizes the importance of considering all real numbers to ensure all possible inputs are included.

What does the domain of a function refer to?

• The range of Y values

• The valid inputs or X values

• The slope of the graph

• The intercepts of the graph

Which of the following is true about the domain of an exponential function?

• It only includes negative numbers

• It only includes positive numbers

• It includes both positive and negative numbers

• It only includes whole numbers

Why are all real numbers considered valid inputs for the exponential function?

• Because the function is only defined for integers

• Because both decimals and fractions are valid inputs

• Because only whole numbers are valid

• Because decimals and fractions are not valid

What is the difference between integers and real numbers in the context of function inputs?

• Integers include decimals, real numbers do not

• Real numbers include decimals, integers do not

• Both include decimals

• Neither include decimals

Which of the following is a valid input for the exponential function discussed?

• Only whole numbers

• Only negative numbers

• Any real number, including decimals

• Only positive numbers

What conclusion does Gabriella reach about the domain of the exponential function?

• It is limited to integers

• It excludes negative numbers

• It includes all real numbers

• It excludes decimals