Understanding Odd and Even Functions

The video tutorial explores the characteristics of odd and even functions using polynomial examples. It begins with a function 2x^3 - x, identifying it as an odd and increasing function. The tutorial then examines a function with an exponent of four, classifying it as an even function with specific x-intercepts and minimum values. The impact of changing coefficients from positive to negative is analyzed, showing how it affects the graph's behavior. Finally, the tutorial discusses an odd function with a negative leading coefficient, highlighting its decreasing nature and identifying zeros.

What is the behavior of the function 2x^3 - x as described in the video?

• It starts low on the left and ends low on the right.

• It starts high on the left and ends high on the right.

• It starts low on the left and ends high on the right.

• It starts high on the left and ends low on the right.

Why is the function 2x^3 - x considered an odd function?

• Because it has no x-intercepts.

• Because its tails go in opposite directions.

• Because it has a positive leading coefficient.

• Because it has an even exponent.

What is the highest exponent in the function 2x^4?

• 2

• 3

• 4

• 5

What is the end behavior of the function 2x^4?

• Up on both sides.

• Down on both sides.

• Down on the left and up on the right.

• Up on the left and down on the right.

What happens to the function 2x^4 when the coefficient is changed to -2?

• It becomes an odd function.

• It becomes a constant function.

• It remains an even function but goes down on both sides.

• It remains an even function but goes up on both sides.

Why does the function -2x^4 go down on both sides?

• Because it has an odd exponent.

• Because it has a positive leading coefficient.

• Because it has no x-intercepts.

• Because it has a negative leading coefficient.

What is the highest exponent in the function -x^7?

• 5

• 6

• 7

• 8

What is the behavior of the function -x^7?

• It starts low on the left and ends high on the right.

• It starts high on the left and ends high on the right.

• It starts high on the left and ends low on the right.

• It starts low on the left and ends low on the right.

Why is the function -x^7 considered an odd function?

• Because it has an even exponent.

• Because it has a positive leading coefficient.

• Because it has no x-intercepts.

• Because its tails go in opposite directions.

Where is the zero of the function -x^7 located?

• At x = 0.5

• At the origin

• At x = -1

• At x = 1