Exponential Characteristics

Key Features of Exponential Functions

Algebra 2 Unit 6 (Lesson 1)

Exponential Function

Subject | Subject

Some text here about the topic of discussion

​Identifying Features of Exponential Functions

Multiple Choice

Is this an exponential growth or decay function?

$$f\left(x\right)=18\left(1.04\right)^x$$  

• growth

• decay

Multiple Choice

What is the growth factor of this exponential function?

$$f\left(x\right)=18\left(1.04\right)^x$$  

• 18

• 1.04

• 1

• 0.04

Identifying Growth and Decay rates

​

2. Identify the growth or decay factor

3. Determine if it is growth or decay

   1. If the factor is less than 1, it is decay.

   2. If the factor is greater than 1, it is growth.

4. ​Solve for r.​

Some text here about the topic of discussion

Multiple Choice

What is the growth rate of this exponential function?

$$f\left(x\right)=18\left(1.04\right)^x$$  

• 18

• 1.04

• 1

• 0.04

Fill in the Blank

What is the rate of change (growth or decay) for this exponential function?

$$f\left(x\right)=27\left(0.84\right)^x$$  

Fill in the Blank

What is the rate of change (growth or decay) for this exponential function?

$$f\left(x\right)=13\left(1.09\right)^x$$  

​A stock is purchased for $35. Its value increases by 50% each year.

​

Model this scenario using an exponential equation.

​Example in Modeling with Exponential Functions

​increasing by 50% means that this is an exponential growth function

​2 to the power of any number will never be zero. It is get infinitely close to zero, but never actually zero. This is why you have a curved bracket, because zero is not included by everything greater than it is.

​

​There is not an x-intercept, only a y-intercept

​This end behavior notation means:

"as x approaches negative infinity, y approaches 0 and as x approaches infinity, y approaches infinity"​

Multiple Choice

What is the domain of the function?

$$g\left(x\right)=5\left(\frac{1}{2}\right)^x$$  

• $$\left(-\infty,\infty\right)$$  

• $$\left[-\infty,\infty\right]$$  

• $$\left(0,\infty\right)$$  

• $$\left(-\infty,0\right)$$  

​The "left" and "right" sides of the graph extend infinitely with no breaks or asymptotes in the middle.

Multiple Choice

What is the range of the function?

$$g\left(x\right)=5\left(\frac{1}{2}\right)^x$$  

• $$\left(-\infty,\infty\right)$$  

• $$\left[-\infty,\infty\right]$$  

• $$\left(0,\infty\right)$$  

• $$\left(-\infty,0\right)$$  

Multiple Choice

What is the intercept of the function?

$$g\left(x\right)=5\left(\frac{1}{2}\right)^x$$  

• (5, 0) 

•  (0, 5)

•  (0, 0)

• (5, 1) 

​The graph never touches or crosses the x-axis. It only crosses the y-axis at 5.

Multiple Choice

What is the asymptote of the function? $$g\left(x\right)=5\left(\frac{1}{2}\right)^x$$  

• $$y=\infty$$  

• $$x=0$$  

• $$y=0$$  

• $$x=-\infty$$  

​The graph approaches the x-axis infinitely but will never touch or cross.

​

y = ? is the equation for horizontal lines​

Multiple Choice

What is the end behavior of the function? $$g\left(x\right)=5\left(\frac{1}{2}\right)^x$$  

• $$x\rightarrow-\infty,\ y\rightarrow\infty$$   $$x\rightarrow\infty,\ y\rightarrow-\infty$$  

•   $$x\rightarrow-\infty,\ y\rightarrow0$$   $$x\rightarrow\infty,\ y\rightarrow\infty$$  

•   $$x\rightarrow-\infty,\ y\rightarrow\infty$$   $$x\rightarrow\infty,\ y\rightarrow0$$  

•   $$x\rightarrow-\infty,\ y\rightarrow-\infty$$   $$x\rightarrow\infty,\ y\rightarrow\infty$$  

​The graph goes up to infinity on the left which is where x approaches negative infinity.

​

The graph approaches 0 on the right which is where x approaches infinity.​

​Try Example 1 on page 140 in your workbook by yourself. Check your work on the next slide.

Open Ended

Did you get Example 1 correct when you tried it on your own?

If you did not, what part of the problem was confusing or did not make sense?