Understanding the Domain and Graphing of a Function

The video tutorial explains how to determine the domain of a function involving a square root, complete a table of values for graphing, and plot the function on a graph. It covers the importance of selecting x-values that result in perfect squares under the square root to simplify calculations. The tutorial also demonstrates how to use a graphing calculator to verify the graph and table of values, highlighting the function's horizontal and vertical shifts.

What is the domain of the function f(x) = √(x + 2) - 3?

• x ≤ -2

• x ≥ -2

• x > -2

• x < -2

What happens to the function f(x) = √(x + 2) - 3 at x = -2?

• The function is undefined

• The function starts

• The function ends

• The function is at its maximum

Why do we select specific x-values such as -2, -1, 2, and 7 for graphing?

• To avoid negative numbers

• To simplify the function

• To ensure the function is linear

• To make the radicand a perfect square

Which x-value results in the radicand being 4 for the function f(x) = √(x + 2) - 3?

• x = 6

• x = 0

• x = 2

• x = 4

What is the y-value when x = 2 for the function f(x) = √(x + 2) - 3?

• -3

• -2

• 0

• -1

What is the y-coordinate when x = 7 for the function f(x) = √(x + 2) - 3?

• 0

• -1

• -2

• -3

How does the function f(x) = √(x + 2) - 3 transform the basic square root function?

• Shifted right 2 units and down 3 units

• Shifted left 2 units and up 3 units

• Shifted left 2 units and down 3 units

• Shifted right 2 units and up 3 units

What does the -3 at the end of the function f(x) = √(x + 2) - 3 represent?

• A reflection

• A vertical shift

• A stretch

• A horizontal shift

What is the purpose of using a graphing calculator in this context?

• To find the domain

• To calculate the derivative

• To verify the graph and table of values

• To solve the function

How can you verify the table of values using a graphing calculator?

• By checking the domain

• By plotting the points manually

• By using the table function

• By calculating the derivative