Understanding Exponential Functions

The video tutorial explains how to match equations to graphs by identifying exponential functions. It covers the concept of initial value, which is the y-intercept, and distinguishes between exponential growth and decay based on the base value. The tutorial guides viewers through matching equations to graphs by analyzing the initial value and the base, explaining that a base between 0 and 1 indicates decay, while a base greater than 1 indicates growth. The video concludes with examples of matching equations to specific graphs based on these characteristics.

What does the initial value 'A' represent in an exponential function?

• The slope of the graph

• The y-intercept of the function

• The maximum value of the function

• The x-intercept of the function

In an exponential function, what does it mean if the base 'B' is between 0 and 1?

• The function is linear

• The function is constant

• The function represents exponential decay

• The function represents exponential growth

If 'A' is greater than 1 in an exponential function, what can be inferred about the graph?

• It will represent exponential growth

• It will represent exponential decay

• It will be a linear function

• It will have a y-intercept of 0

What is the y-intercept of a function with an initial value 'A' of 4?

• 1

• 0

• 3

• 4

Which graph characteristic indicates a smaller value of 'B' in exponential decay?

• The graph is vertical

• The graph is horizontal

• The graph is flatter

• The graph is steeper

Which equation would match a graph with a base 'B' of 0.5?

• The graph with the steepest decline

• The graph with the flattest incline

• The graph with the flattest decline

• The graph with the steepest incline

If two graphs have the same initial value 'A', what can be said about their y-intercepts?

• They have different y-intercepts

• They have the same y-intercept

• One has a y-intercept of one

• One has a y-intercept of zero

What does a base 'B' greater than 1 indicate in an exponential function?

• The function is decreasing

• The function is constant

• The function is increasing

• The function is linear

Which graph would correspond to an equation with a base 'B' of 1.5?

• The graph with the fastest decrease

• The graph with the slowest decrease

• The graph with the fastest increase

• The graph with the slowest increase

Which graph would match an equation with a base 'B' of 1.2?

• The graph with the slowest increase

• The graph with the fastest decrease

• The graph with the fastest increase

• The graph with the slowest decrease