Exploring Exponential Functions and Their Equations

This video tutorial covers exponential functions, focusing on writing equations from tables, understanding domain and range, and identifying key features like the common ratio. It explains the parent function, the significance of the initial amount and common ratio, and how to determine if a function represents growth or decay. The video also provides examples and practice problems to reinforce these concepts.

What is the parent function of an exponential function?

• a + bx

• a - bx

• a * b^x

• a / b^x

What does the variable 'a' represent in the exponential function a * b^x?

• The slope

• The exponent

• The initial amount or y-intercept

• The common ratio

How do you determine the common ratio from a table of exponential values?

• Subtract the first term from the second term

• Add the first term to the second term

• Divide the second term by the first term

• Multiply the first term by the second term

If the common ratio (B) is between 0 and 1, what type of exponential function is it?

• Exponential growth

• Linear decay

• Exponential decay

• Linear growth

Where is the y-intercept located in an exponential function?

• Where y equals 1

• Where x equals 1

• Where y equals 0

• Where x equals 0

What is the domain of an exponential function?

• All negative numbers

• All positive numbers

• All real numbers

• All integers

What is the range of an exponential function?

• y is all real numbers

• y is less than 0

• y is greater than 0

• y is equal to 0

What is the asymptote of an exponential function?

• x = 0

• y = 0

• x = 1

• y = 1

If the common ratio is 4 and the y-intercept is 1.5, what is the exponential function?

• f(x) = 1.5 * 4^x

• f(x) = 4 + 1.5^x

• f(x) = 4 * 1.5^x

• f(x) = 1.5 + 4^x

How do you find the y-intercept if it is not given in the table?

• Divide the first term by the common ratio

• Multiply the first term by the common ratio

• Add the first term to the common ratio

• Subtract the first term from the common ratio