Cubic Function Graphing Concepts

The video tutorial explains how to graph cubic functions using four steps. It begins with a comparison between quadratic and cubic functions, highlighting the differences in their behavior due to the number of negatives. The tutorial then outlines the four steps: finding x-axis intercepts, finding y-axis intercepts, selecting critical points, and sketching the graph. Examples are provided to illustrate these steps, and the use of a graphing calculator is demonstrated to verify results.

How does a quadratic function behave when a negative number is squared?

• It becomes negative

• It remains negative

• It becomes positive

• It remains unchanged

What is a key difference between quadratic and cubic functions?

• Cubic functions always change direction

• Quadratic functions are always positive

• Cubic functions never change direction

• Quadratic functions have no intercepts

What happens to the sign of a cubic function when it has an odd number of negatives?

• The function becomes undefined

• The function becomes zero

• The sign switches

• The sign remains the same

What is the first step in graphing a cubic function?

• Find the y-axis intercepts

• Identify the critical points

• Determine the x-axis intercepts

• Use a graphing calculator

When finding the x-axis intercepts, what value is set to zero?

• The coefficient

• y

• x

• The slope

What is the y-axis intercept when x equals zero?

• The intercept is undefined

• The intercept is always zero

• The intercept is the coefficient of x

• The intercept is the constant term

Why are critical points important in graphing cubic functions?

• They show the direction of the curve

• They are not important

• They help find intercepts

• They determine the slope

What tool can be used to verify the graph of a cubic function?

• A protractor

• A graphing calculator

• A ruler

• A compass

What is the result of plugging in x = 1 in the cubic function example?

• The result is 1

• The result is 6

• The result is -6

• The result is 0

What is the significance of the point (-3, -10) in the cubic function graph?

• It is a minimum point

• It is a maximum point

• It shows a change in direction

• It is an intercept