Lesson 1 Attributes of Cubic Functions

Attributes of Cubic Functions

​TEKS 2A.2A
We will analyze graphs to determine attributes of cubic functions.

I will summarize how to determine attributes of cubic functions from their graphs.

Poll

What is an example of an attribute in any function?

• The function itself

• The x and y intercepts

• Solving for x

• Transformations

This is a point of a curve which a change in the direction of curvature occurs.

​

Vocab:
Inflection Point

​Please note all cubic functions have Rotational Symmetry about their

inflection point.

 

Multiple Choice

From your notes, which of the following is the correct attribute of the cubic parent function?

• Y-intercept of 5
• Domain and Range is all real numbers

• X-intercept of -1

• Rotational symmetry about the intercepts

Step 1. Graph function on Desmos.com

Step 2. Identify x-intercept, y- intercept, and inflection point by tracing the graph

Step 3. State rotational symmetry about inflection point

Step 4. State domain and range

Step 5. Check the equation/function values over the given interval to determine and state the min and max values {y-values always}

Let's graph some examples!

​Domain and Range in Interval Notation

Multiple Choice

What did you get for the max and min on the given interval for Example 1? (Remember max and min are the Y-values)

• Max: -4

  Min: 32

• Max: -2

  Min: 1

• Max: 34

  Min: -1

• Max: 32

  Min: -4

​Domain and Range in Interval Notation

Dropdown

The x-intercept is

Select answer

the y-intercept is ​

Select answer

the inflection point is ​​

Select answer

and the Domain and Range is ​

Select answer

​Domain and Range in Inequality Notation

Labelling

Label the attributes on the graph from your notes.

Drag labels to their correct position on the image

Max: y = 343

Max: y = 2744

Rotational Symmetry (0,5)

x and y -intercept (0,0)

​Domain and Range in Inequality Notation

Poll

Rate your understanding of attributes for Cubic functions on a scale of 1-5, 1 being totally lost and 5 being completely confident.

• 5 - Oh yeah I got this!

• 4 - I feel pretty good

• 3 - I need a little more practice

• 2 - Ummm Maybe I get it

• 1 - Help! What is this madness?