Understanding Exponent Rules and Functions

The video tutorial explores the concepts of increasing and decreasing functions through exponent rules. It begins by discussing how to interpret negative signs in expressions and proceeds to rewrite expressions to fit the form a times b to the x power. The tutorial explains how to determine if a function is increasing or decreasing based on the base value. It also covers manipulating exponents using rules and converting negative exponents to positive ones. The tutorial emphasizes understanding exponent rules for confidence in solving related problems.

What initial assumption might one make about a function with a negative sign?

• It is decreasing.

• It is increasing.

• It is constant.

• It is undefined.

Which of the following is NOT an exponent rule?

• Moving a negative exponent to the denominator to make it positive.

• Reversing exponent rules to manipulate expressions.

• Adding exponents when bases are different.

• Multiplying exponents when bases are the same.

In the expression a * b^x, what does 'a' represent?

• The base of the exponent.

• The rate of change.

• The exponent itself.

• The initial amount or y-intercept.

If the base 'b' in a * b^x is greater than 1, what can be said about the function?

• It is constant.

• It is increasing.

• It is undefined.

• It is decreasing.

What is the first step in rewriting an expression to fit the form a * b^x?

• Identify the base 'b'.

• Identify the initial amount 'a'.

• Move the exponent to the denominator.

• Combine all exponents.

What does the expression a * b^x represent in terms of function behavior?

• An exponential function.

• A constant function.

• A linear function.

• A quadratic function.

What happens to a negative exponent when it is moved to the denominator?

• It doubles in value.

• It remains negative.

• It becomes positive.

• It becomes zero.

Which of the following is a correct way to rewrite a negative exponent?

• Add it to the base.

• Move it to the denominator and make it positive.

• Leave it as is.

• Move it to the numerator.

What is the significance of the base 'b' being between 0 and 1 in a * b^x?

• The function is increasing.

• The function is decreasing.

• The function is constant.

• The function is undefined.

What is the result of combining exponents with the same base?

• Divide the exponents.

• Subtract the exponents.

• Multiply the exponents.

• Add the exponents.