Square Root Functions and Inequalities

This 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 undefined, and demonstrates how to set the expression inside the square root greater than or equal to zero to find valid x-values. The tutorial covers graphing both positive and negative square root functions, and explains how to identify the domain and range for each. It also includes examples of more complex square root functions with transformations.

What is the first step in determining the domain of a square root function?

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

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

• Set the expression inside the square root to be equal to zero.

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

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

• 3

• 2

• 5

• 4

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

• By looking at the X values.

• By looking at the Y values.

• By looking at the Z values.

• By looking at the W values.

What happens to the inequality when you divide by a negative number?

• It becomes undefined.

• It flips direction.

• It stays the same.

• It becomes an equation.

In the function y = 2√(-x), what is the domain?

• X is less than or equal to zero.

• X is less than zero.

• X is greater than zero.

• X is greater than or equal to zero.

What is the effect of adding a constant outside the square root function?

• It shifts the graph horizontally.

• It shifts the graph vertically.

• It stretches the graph.

• It compresses the graph.

For the function h(x) = -5√(x+4) - 1, what is the domain?

• X is less than or equal to 4.

• X is greater than or equal to 4.

• X is less than or equal to -4.

• X is greater than or equal to -4.

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

• Y is less than or equal to 1.

• Y is less than or equal to -1.

• Y is greater than or equal to -1.

• Y is greater than or equal to 1.

What is the Y value when X is 0 in the function h(x) = -5√(x+4) - 1?

• 0

• -11

• -6

• -1

How does the graph of a square root function with a negative coefficient differ from one with a positive coefficient?

• It is reflected over the X-axis.

• It is reflected over the Y-axis.

• It is shifted to the left.

• It is shifted to the right.