Understanding Square Root Functions and Their Transformations

This video tutorial covers graphing the square root function and its vertical and horizontal translations. It begins with the basic square root function, explaining how to find its domain and graph it using a table of values. The tutorial then explores vertical translations by adding or subtracting a constant to the function, resulting in upward or downward shifts. Finally, it examines horizontal translations by adding or subtracting a constant inside the square root, causing left or right shifts. The video emphasizes understanding these transformations and provides examples to illustrate the concepts.

What is the domain of the basic square root function f(x) = √x?

• x ≥ 0

• x ≤ 0

• x > 0

• x < 0

Which of the following points is on the graph of the basic square root function?

• (5, 3)

• (4, 2)

• (3, 3)

• (2, 2)

How does the graph of g(x) = √x + 2 differ from the basic square root function?

• It shifts 2 units to the left.

• It shifts 2 units down.

• It shifts 2 units to the right.

• It shifts 2 units up.

What is the effect of subtracting a positive number from the square root function, as in h(x) = √x - 2?

• The graph shifts 2 units down.

• The graph shifts 2 units to the right.

• The graph shifts 2 units up.

• The graph shifts 2 units to the left.

In the function g(x) = √(x + 2), what is the new domain?

• x ≥ -2

• x > -2

• x ≥ 2

• x > 2

How does the graph of g(x) = √(x + 2) compare to the basic square root function?

• It shifts 2 units to the left.

• It shifts 2 units to the right.

• It shifts 2 units down.

• It shifts 2 units up.

What is the effect of the transformation h(x) = √(x - 2) on the graph?

• The graph shifts 2 units to the right.

• The graph shifts 2 units down.

• The graph shifts 2 units to the left.

• The graph shifts 2 units up.

If a function is transformed by y = f(x + c), where c is positive, what happens to the graph?

• It shifts down c units.

• It shifts up c units.

• It shifts right c units.

• It shifts left c units.

What is the transformation for y = f(x - c) where c is positive?

• Shift left c units

• Shift right c units

• Shift up c units

• Shift down c units

How can you determine the transformation of a square root function by looking at its equation?

• By identifying the coefficients of x

• By observing the leading coefficient

• By analyzing the constants added or subtracted

• By checking the degree of the function