Exploring Transformation of Functions: Cubic, Square Root, and Piecewise

What is the rule for the new function introduced in the video?

• Subtract the input from itself three times

• Add the input to itself three times

• Multiply the input by itself three times

• Multiply the input by itself two times

What is the output when the input is -2 for the cubic function?

• 8

• -8

• 4

• -4

What is the domain of the square root function?

• All real numbers

• Negative numbers

• Positive numbers excluding zero

• Positive numbers including zero

Why are negative numbers not included in the domain of the square root function?

• They produce positive outputs

• They produce zero outputs

• They produce no outputs

• They produce undefined outputs

What is the range of the cubic function?

• Positive numbers excluding zero

• Negative numbers

• Positive numbers including zero

• All real numbers

Does the cubic function pass the horizontal line test?

• No, because it does not intersect the x-axis

• No, because there are repeats in the outputs

• Yes, because there are no repeats in the outputs

• Yes, because it intersects the x-axis multiple times

What is the vertex of the square root curve?

• (0,0)

• (-1,-1)

• (1,1)

• (2,2)

What is the end behavior of the square root function?

• As x approaches infinity, y approaches negative infinity

• As x approaches infinity, y approaches infinity

• As x approaches negative infinity, y approaches infinity

• As x approaches negative infinity, y approaches negative infinity

What is the domain of the piecewise function discussed?

• All real numbers

• Numbers from -4 to 3

• Numbers from 0 to 4

• Numbers from -3 to 4

What is the vertical shift of the transformed blue function in the piecewise example?

• Shifted down by 2 units

• Shifted up by 2 units

• Shifted left by 2 units

• Shifted right by 2 units