Cubic Function Transformations

The video tutorial covers graphing cubic functions, starting with the parent function and its properties, including domain, range, and end behavior. It then explores various transformations such as reflection, stretch, compression, and shifts, and how these affect the graph. The tutorial also demonstrates graphing transformed functions and analyzing their changes. Finally, it explains how to work backwards from a graph to determine the equation using reference points and symmetry.

What is the primary focus of section 5.1 in graphing cubic functions?

• Graphing linear functions

• Understanding quadratic functions

• Graphing cubic functions and transformations

• Exploring exponential functions

Which of the following is a reference point for the parent cubic function?

• (2, 8)

• (-1, -1)

• (3, 27)

• (0, 1)

What is the domain of the parent cubic function?

• Only integers

• All real numbers

• All negative numbers

• All positive numbers

As x approaches positive infinity, what happens to the y-values of the parent cubic function?

• They increase to positive infinity

• They remain constant

• They approach zero

• They decrease to negative infinity

What is the range of the parent cubic function?

• Only integers

• All real numbers

• All negative numbers

• All positive numbers

What happens to the y-values as x approaches negative infinity in the parent cubic function?

• They increase to positive infinity

• They approach zero

• They decrease to negative infinity

• They remain constant

What type of transformation occurs when 'a' is negative in a cubic function?

• Vertical compression

• Reflection across the x-axis

• Horizontal shift

• Vertical stretch

What is the effect of a positive 'H' in the transformation of a cubic function?

• Move left

• Reflect across the y-axis

• Reflect across the x-axis

• Move right

What is the effect of a negative 'H' in the transformation of a cubic function?

• Reflect across the y-axis

• Move left

• Reflect across the x-axis

• Move right

What is the effect of a fraction between 0 and 1 as 'a' in a cubic function?

• Reflection across the x-axis

• Vertical stretch

• Horizontal shift

• Vertical compression