Graphing Radical Functions Explained

The video tutorial covers graphing radical functions, focusing on square and cube root functions. It explains the domain and range of these functions, emphasizing the restrictions for square roots. The tutorial also discusses transformations, including translations and reflections, and their impact on the graph. Through examples, it demonstrates how to graph these functions and adjust for vertical and horizontal shifts. The lesson concludes with practice problems and a summary of key concepts.

What are the parent functions discussed for graphing radical functions?

• Sine of x, Cosine of x

• Square of x, Cube of x

• Log of x, Exponent of x

• Square root of x, Cube root of x

Why is the domain of the square root function restricted?

• Square roots cannot be calculated

• Square roots are undefined for positive numbers

• Square roots always result in negative numbers

• Square roots of negative numbers are imaginary

What is the range of the square root parent function?

• No specific range

• y is greater than or equal to 0

• y is less than or equal to 0

• All real numbers

Which transformations do not affect the domain and range of a radical function?

• Rotations and reflections

• Stretching and shrinking

• Reflections and translations

• Vertical and horizontal shifts

What happens to the square root function when it undergoes a vertical shift down by 5 units?

• Starts at (0, 5)

• Starts at (0, -5)

• Starts at (-5, 0)

• Starts at (5, 0)

After a vertical shift of 5 units down, what is the new range of the function?

• y is greater than or equal to -5

• y is less than or equal to -5

• y is greater than or equal to 0

• y is less than or equal to 0

What is the effect of a horizontal shift to the left by 3 units on the domain of the function?

• x is less than or equal to 0

• x is greater than or equal to 0

• x is less than or equal to -3

• x is greater than or equal to -3

How does a vertical shrink affect the growth rate of the function?

• It grows faster

• It grows slower

• It grows at the same rate

• It does not grow

What is the range of the function after a vertical shrink and horizontal shift?

• y is greater than or equal to 0

• No specific range

• y is less than or equal to 0

• All real numbers

What transformation results in the graph being flipped upside down?

• Reflection across the x-axis

• Horizontal shift left

• Vertical shift up

• Vertical shrink