Left and Right hand behavior - Learn Math Online

The video tutorial explains how to determine the left and right hand behavior of functions, focusing on the concept of end behavior in graphs. It covers the Cartesian coordinate system, parent functions, and reflections. The tutorial provides a detailed analysis of end behavior based on the degree and leading coefficient of polynomials, and includes problem-solving examples to illustrate these concepts.

Why is understanding the end behavior of a graph important?

• It is necessary for finding the graph's intercepts.

• It is crucial for calculating the graph's area.

• It assists in predicting the graph's direction and form.

• It helps in determining the graph's symmetry.

In the Cartesian coordinate system, what does the x-axis represent?

• The output values of the function

• The domain of the function

• The range of the function

• The intercepts of the function

What is the significance of using f(x) instead of y in functions?

• It represents the output value of a function.

• It simplifies the graphing process.

• It distinguishes between different types of graphs.

• It indicates the function's degree.

How does a negative leading coefficient affect the graph of a quadratic function?

• The graph becomes a straight line.

• The graph remains unchanged.

• The graph opens downwards.

• The graph opens upwards.

What happens to the end behavior of a cubic function with a positive leading coefficient?

• It rises to the left and falls to the right.

• It falls to the left and rises to the right.

• It forms a parabola.

• It remains constant.

What determines whether both ends of a graph rise or fall?

• The function's intercepts

• The leading coefficient's sign

• The function's degree

• The graph's symmetry

For a polynomial with an even degree and a positive leading coefficient, what is the end behavior?

• Both ends rise.

• Both ends fall.

• The graph remains constant.

• One end rises, the other falls.

What is the end behavior of a polynomial with an odd degree and a negative leading coefficient?

• Both ends fall.

• Both ends rise.

• Falls to the left, rises to the right.

• Rises to the left, falls to the right.

In the example of a polynomial with a leading term of -x^2, what is the end behavior?

• Falls to the left, rises to the right.

• Both ends fall.

• Rises to the left, falls to the right.

• Both ends rise.

How does the degree of a polynomial affect its end behavior?

• It changes the graph's color.

• It influences whether the graph's ends rise or fall.

• It affects the graph's symmetry.

• It determines the graph's intercepts.