Exponential Functions Mastery Challenge

This video tutorial covers the basics of exponential functions, focusing on their equations, graphs, and characteristics. It explains the concept of y-intercept and growth rate, comparing functions with different growth rates. The video also introduces exponential decay, highlighting how functions decrease when the growth rate is between 0 and 1. Key concepts such as horizontal asymptotes and the behavior of exponential functions are summarized.

What is the y-intercept of the exponential function y = 1 * 2^x?

• 0

• 4

• 1

• 2

In the function y = 1 * 2^x, what does the number 2 represent?

• Growth rate

• Base

• Exponent

• Y-intercept

If the growth rate of an exponential function is 3, how does the graph behave compared to a function with a growth rate of 2?

• It remains constant

• It increases more slowly

• It decreases

• It increases more quickly

What is the y-intercept of the function y = 4 * (1/2)^x?

• 4

• 3

• 2

• 1

How does the graph of y = 4 * (1/2)^x behave?

• It oscillates

• It decreases from left to right

• It remains constant

• It increases from left to right

What happens to the y-values in an exponential decay function?

• They oscillate

• They remain constant

• They decrease

• They increase

What is the standard form of an exponential function?

• y = a * b^x

• y = a + bx

• y = a / b^x

• y = ax + b

What is the term for the value 'a' in the exponential function y = a * b^x?

• Base

• Initial value

• Exponent

• Growth rate

If the base 'b' in an exponential function is between 0 and 1, what is the function doing?

• Remaining constant

• Oscillating

• Decaying

• Growing

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

• A point where the graph ends

• A line the graph approaches but never touches

• A line the graph crosses

• A point where the graph starts