Understanding Exponential and Linear Functions

This video tutorial continues from lesson 24, focusing on exponential functions. It explains how to find the equation of an exponential function given two points on a graph. The tutorial covers setting up and solving systems of equations, handling negative exponents, and understanding the concepts of domain, range, and asymptotes. Example problems are provided to illustrate these concepts, and the video concludes with a comparison of linear and exponential functions.

What is the first step in finding the equation of an exponential function given two points?

• Start with the first coordinate

• Find the y-intercept

• Start with the second coordinate

• Calculate the slope

In the equation y = a * b^x, what does 'b' represent?

• The y-intercept

• The base of the exponential function

• The x-intercept

• The slope of the line

How do you solve for 'b' in the system of equations for exponential functions?

• Divide the equations

• Multiply the equations

• Add the equations

• Subtract the equations

What is the value of 'a' if b^0 equals 1?

• 10

• 1

• 0

• 5

In the example without a y-intercept, what is the first coordinate used?

• (0, 5)

• (1, 10)

• (4, 12)

• (3, 1)

What is the value of 'b' when solving the example without a y-intercept?

• 1/12

• 12

• 1/8

• 8

In the practice problem, what is the coordinate for X = 1?

• (2, 18)

• (2, 12)

• (1, 18)

• (1, 12)

What is the value of 'b' in the practice problem with negative exponents?

• 2

• 5

• 3

• 4

What is a horizontal asymptote in the context of exponential functions?

• The y-intercept

• A line the graph approaches but never touches

• A line the graph crosses

• The x-intercept

What is the domain of an exponential function?

• All positive numbers

• All negative numbers

• All real numbers

• All integers