Exponential Functions and Their Properties

The video introduces exponential functions, comparing them with polynomial functions like x^2. It explains how to graph these functions, focusing on the differences between x^2 and 2^x. The video covers negative exponents, demonstrating calculations for 2^-3. It then plots the graph of 2^x, highlighting its exponential growth. The formal definition of exponential functions is provided, and examples are given to identify such functions, distinguishing them from non-examples.

What is the main difference between polynomial and exponential functions?

• Polynomial functions have a constant base.

• Exponential functions have a variable base.

• Polynomial functions have a variable exponent.

• Exponential functions have a constant base and variable exponent.

Which of the following is a polynomial function?

• h(x) = 5^x

• f(x) = 2^x

• G(x) = x^2

• k(x) = 3^x

What does the graph of G(x) = x^2 look like?

• A straight line

• A parabola

• An exponential curve

• A circle

What is 2 to the power of -3?

• 1/2

• 1/8

• 8

• 1/4

How do you calculate 2 to the power of a negative exponent?

• Multiply by the base

• Add the base

• Take the reciprocal of the base raised to the positive exponent

• Divide by the base

What is the value of 2^0?

• Undefined

• 1

• 0

• 2

Which point is always on the graph of an exponential function with base 2?

• (0, 1)

• (1, 0)

• (1, 1)

• (0, 0)

What happens to the graph of 2^x as x becomes more negative?

• It approaches the x-axis.

• It becomes a parabola.

• It moves away from the x-axis.

• It becomes a straight line.

What is the general shape of an exponential function graph?

• Linear

• Parabolic

• Exponential curve

• Circular

Which of the following is an exponential function?

• g(x) = 5^x

• f(x) = x^3

• k(x) = x^2 + 3x + 2

• h(x) = x + 7