Transformations and Properties of Exponents

Mr. Bean's lesson covers various properties of exponents, including negative exponents, product property, and power property. The video explains how these properties apply to exponential functions, focusing on horizontal translation and dilation. It also discusses reflections over axes and the concept of the Kth root, providing examples and problem-solving techniques.

What is the result of raising a base to a negative exponent?

• The base remains unchanged

• The reciprocal of the base raised to the positive exponent

• The base becomes negative

• The base becomes zero

When multiplying two exponents with the same base, what should you do with the exponents?

• Multiply them

• Subtract them

• Add them

• Divide them

What does a horizontal translation of an exponential function affect?

• The y-values

• The x-values

• The slope of the graph

• The intercept of the graph

How does a horizontal translation relate to a vertical dilation?

• Horizontal translation is the inverse of vertical dilation

• Horizontal translation is twice the effect of vertical dilation

• They are unrelated

• They are equivalent

In a transformation problem, what does a shift left in the exponent indicate?

• A vertical shift up

• A vertical shift down

• A horizontal shift right

• A horizontal shift left

What is the power property of exponents?

• Divide the exponents

• Subtract the exponents

• Multiply the exponents

• Add the exponents

What happens when you multiply the x-value by a negative in a function?

• Shift down

• Reflect over the x-axis

• Shift up

• Reflect over the y-axis

What is the kth root of a number?

• The number raised to the power of 1/k

• The number multiplied by k

• The number divided by k

• The number raised to the power of k