Square Root Functions and Their Properties

The video tutorial teaches how to graph square root functions, focusing on determining the domain and range. It explains that the square root of a negative number is not possible, and demonstrates how to set the domain by ensuring the expression inside the square root is non-negative. The tutorial uses X-Y tables to find points for graphing and shows how to plot these points to form the graph. It also covers graphing functions with negative X values and provides an example of a more complex square root function. The video concludes with a discussion on domain and range, emphasizing their importance in graphing.

What is the main restriction when graphing square root functions?

• You cannot take the square root of zero.

• You cannot take the square root of a negative number.

• You cannot take the square root of a positive number.

• You cannot take the square root of a fraction.

How do you determine the domain of a square root function?

• By setting the expression inside the square root to be less than or equal to zero.

• By setting the expression inside the square root to be greater than or equal to zero.

• By setting the expression inside the square root to be greater than zero.

• By setting the expression inside the square root to be less than zero.

Which of the following is a perfect square root that can be used in the X-Y table?

• 2

• 3

• 5

• 4

What is the shape of the graph of a square root function?

• Half a parabola

• A straight line

• A full parabola

• A circle

How is the range of a square root function determined?

• By the X values

• By the Y values

• By the T values

• By the Z values

When graphing a square root function with a negative X, what must you do to the inequality?

• Add a constant

• Subtract a constant

• Flip the inequality sign

• Keep it the same

What is the domain of the function y = 2√(-x)?

• X is less than or equal to zero

• X is greater than zero

• X is less than zero

• X is greater than or equal to zero

In the function H(x) = -5√(x + 4) - 1, what is the first step to find the domain?

• Set x + 4 less than zero

• Set x + 4 greater than or equal to zero

• Set x + 4 less than or equal to zero

• Set x + 4 greater than zero

What is the range of the function H(x) = -5√(x + 4) - 1?

• Y is greater than -1

• Y is greater than or equal to -1

• Y is less than -1

• Y is less than or equal to -1

What is the effect of the transformation in the function H(x) = -5√(x + 4) - 1?

• It reflects the graph over the Y-axis

• It shifts the graph up

• It shifts the graph down

• It reflects the graph over the X-axis