Introduction to Exponential Equations

​Key Features of Exponential Functions

Today, we will learn what an exponential function is and what its key features are.​

If b is...

• Greater than 1 (b>1), the function is exponential GROWTH

• Less than 1 and greater than 0 (0<b<1) the function is exponential DECAY

​

​Definition of exponential function

​Growth vs Decay

​

Multiple Choice

Which of the following is an exponential function?

• y = x²

• f(x) = 3x³

• y = x³

• f(x) = 3^x

Multiple Choice

Is this exponential growth or decay?

• Growth
• Decay

Multiple Choice

Is the following function an example of decay or growth?

f(x) = 2(1.25)^x

• Exponential Growth

• Exponential Decay

Multiple Choice

Is the pictured graph growth, decay, or linear or none?  

• Exponential Growth
• Exponential Decay

Multiple Choice

Which represents exponential decay?

• A

• B

• C

• D

Domain: all possible x values

​

​D= all real numbers

​

Range: all possible y values

​

R= y>0​

​

Asymptote: Imaginary line that the graph approaches, but never crosses​

​

y=0​

​

​

​

​PARENT FUNCTION ONLY

​Key Features

​

​

Y- Intercept: one y-intercept

​The y-intercept is "a"

y-intercept=1​

​

​

​

X- Intercept​​: NO x-intercepts

​PARENT FUNCTION ONLY

​Key Features

​

Multiple Choice

What is the domain of the function shown?

• All real numbers

• $$y>0$$  

• All real numbers greater than 1

• $$y<0$$  

Multiple Choice

What is the range of the exponential function?

• all real numbers

• y > -1

• y < -1

• x > -1

Multiple Choice

What is the y-intercept of the function?

• 2
• 3
• 1
• -2

Multiple Choice

What is the x-intercept of the exponential function? 

• (0,1)
• (0,0)
• There is not one

Multiple Choice

In an exponential function, what does the 'a' represent? 

• SLOPE
• RATE OF CHANGE
• Y-INTERCEPT
• COMMON RATIO

Multiple Choice

What is the equation of the horizontal asymptote for following exponential function?

• y = -4

• y > -4

• y < -4

• (0, -3)

Multiple Choice

The line shown on the graph is an asymptote for the exponential curve shown on the graph.

• TRUE

• FALSE

Multiple Choice

What is the equation of the horizontal asymptote for following exponential function?

• y = 1

• y = 2

• y > 1

• (0, 2)

Multiple Choice

What is the range of the exponential function?

• all real numbers

• y > 3

• y < 3

• x > 3

Multiple Choice

What are the domain and range of the function/graph?

• Domain: All Real Numbers

  Range: All Real Numbers

• Domain: All Real Numbers

  Range: y < 2

• Domain: All Real Numbers

  Range: y > 2

• Domain: x > 2

  Range: All Real Numbers

Multiple Select

Rate your understanding. How do you feel about your understanding in exponential functions and its key features?

• 4

  
  

  I am an expert. I can explain how to do this. I can teach others

• 3

  I can do this independently. I've got a good understanding.

• 2

  
  

  I can do this with help or an example. There are parts I do not understand

• 1

  I don't understand it yet, but am starting to learn. I need help learning this.