1.3 Lesson: Extrema and End Behavior

Extrema and
End Behavior

Presentation made by Blake Jensen with credit to McGraw Hill Reveal

Multiple Choice

Which of the following is not a function?
Before you answer.... list the x and y intercepts on your white board!

Match

Match each graph to a definition of it!

Discrete

Continuous

Neither Discrete nor Continuous

Odd Function

Even Function

• Discrete

• Continuous

• Neither Discrete nor Continuous

• Odd Function

• Even Function

Open Ended

What do you think Extrema means? Just give your best guess!

The lowest point on a graph!

Minimum

The highest point on a graph!

Maximum

Extrema means Extremes!

Match

Match the following!

Maximum

Minimum

Doesn't have a maximum or minimum

• Maximum

• Minimum

• Doesn't have a maximum or minimum

It's a minimum just not the minimum!

Relative minimum

It's a maximum just not the maximum!

Relative Maximum

Relative though

Labeling

Match the following labels!

Drag labels to their correct position on the image

Absolute Maximum

Absolute minimum

Relative Minimum

Relative maximum

Let's talk about the ends

Some awful notation but easy to use

As x increases, the graph decreases.
As we go right, the graph points down



As x decreases, the graph decreases
As we go left, the graph points down

Going Up or Down

Going Right or Left

The notation form

Match

Match them! See if you can remember

• $$x\rightarrow\infty$$

• $$x\rightarrow-\infty$$

• $$f\left(x\right)\rightarrow\infty$$

• $$f\left(x\right)\rightarrow-\infty$$

As we go right

As we go left

The graph goes up

The graph goes down

• As we go right

• As we go left

• The graph goes up

• The graph goes down

As we go right, the graph goes ____

As we go left the graph goes __

Write it out!

Let's practice one! Try it out!

Multiple Choice

Select the end behavior notation that matches the graph!

• $$x\rightarrow\infty;f\left(x\right)\rightarrow\infty\$$
  $$x\rightarrow-\infty;f\left(x\right)\rightarrow\infty$$

• 
  
  $$x\rightarrow\infty;f\left(x\right)\rightarrow-\infty\ \ \$$ $$x\rightarrow-\infty;f\left(x\right)\rightarrow\infty$$

• $$x\rightarrow\infty;f\left(x\right)\rightarrow\infty$$
  $$x\rightarrow-\infty;f\left(x\right)\rightarrow-\infty$$

• $$x\rightarrow\infty;f\left(x\right)\rightarrow-\infty$$ $$x\rightarrow-\infty;f\left(x\right)\rightarrow-\infty$$