Understanding Exponent Rules and Functions

The video tutorial explores the concepts of increasing and decreasing functions through the lens of exponent rules. It begins by discussing the impact of negative signs on functions and proceeds to demonstrate how to rewrite expressions using exponent rules. The tutorial emphasizes understanding negative exponents and their manipulation to achieve solutions, ultimately showing how these concepts apply to real-world scenarios.

What is the initial thought when seeing a negative exponent in a function?

• The function is undefined.

• The function is increasing.

• The function is decreasing.

• The function is constant.

Which of the following is true about a base 'b' greater than 1 in an exponential function?

• The function is undefined.

• The function is increasing.

• The function is constant.

• The function is decreasing.

What is the first step in rewriting negative x as negative 1 multiplied by x?

• Factor out negative 1.

• Multiply x by zero.

• Divide x by 2.

• Add 1 to x.

What does the 'a' represent in the expression a * b^x?

• The base of the exponent.

• The exponent value.

• The rate of change.

• The initial amount or y-intercept.

What is the purpose of rewriting expressions in the form a * b^x?

• To simplify calculations.

• To determine if the function is increasing or decreasing.

• To find the derivative.

• To solve for x.

How can a negative exponent be rewritten to become positive?

• By adding 1 to the exponent.

• By moving it to the denominator.

• By multiplying by zero.

• By subtracting 1 from the exponent.

Which exponent rule allows you to combine exponents by multiplying them?

• Power of a power rule.

• Product of powers rule.

• Zero exponent rule.

• Quotient of powers rule.

How can you manipulate exponents to rewrite them in unique ways?

• By using the distributive property.

• By subtracting exponents.

• By using exponent rules in reverse.

• By adding exponents together.

What is the effect of a negative exponent on the graph of a function?

• It shifts the graph upwards.

• It reflects the graph across the x-axis.

• It shifts the graph downwards.

• It reflects the graph across the y-axis.

What is the effect of a base 'b' between 0 and 1 in an exponential function?

• The function is undefined.

• The function is constant.

• The function is decreasing.

• The function is increasing.