Understanding Graph Shifts

The video tutorial explains how to match graphs with their corresponding functions by identifying vertical and horizontal shifts. It begins with an introduction to the parent function, f(x) = √x, and discusses how different functions are shifted up, down, left, or right. The tutorial provides a detailed review of vertical and horizontal shifts, using examples to illustrate how constants inside or outside the square root affect the direction of the shift. The video concludes with a practical application of identifying graphs based on these shifts, emphasizing the importance of recognizing shift types without relying on graphing calculators.

What is the parent function identified in the problem?

• f(x) = sqrt(x)

• f(x) = x^2

• f(x) = 1/x

• f(x) = x^3

If a function is shifted up by 3 units, which of the following represents this transformation?

• f(x) = sqrt(x) + 3

• f(x) = sqrt(x + 3)

• f(x) = sqrt(x) - 3

• f(x) = sqrt(x - 3)

What is the effect of adding a constant outside the square root in the function f(x) = sqrt(x) + c?

• Shifts the graph down by c units

• Shifts the graph up by c units

• Shifts the graph right by c units

• Shifts the graph left by c units

What happens to the graph of f(x) = sqrt(x) if the function is changed to f(x) = sqrt(x - 5)?

• It shifts 5 units to the right.

• It shifts 5 units down.

• It shifts 5 units to the left.

• It shifts 5 units up.

In the function f(x) = sqrt(x - c), what does the constant c do to the graph?

• Shifts it down by c units

• Shifts it left by c units

• Shifts it right by c units

• Shifts it up by c units

Which function represents a shift of the parent function f(x) = sqrt(x) down by 2 units?

• f(x) = sqrt(x + 2)

• f(x) = sqrt(x) + 2

• f(x) = sqrt(x - 2)

• f(x) = sqrt(x) - 2

If f(x) = sqrt(x + 3), what is the direction and magnitude of the shift?

• 3 units to the right

• 3 units to the left

• 3 units up

• 3 units down

Which of the following functions represents a shift of the parent function f(x) = sqrt(x) to the left by 4 units?

• f(x) = sqrt(x - 4)

• f(x) = sqrt(x) - 4

• f(x) = sqrt(x + 4)

• f(x) = sqrt(x) + 4

Which function represents a shift of the parent function f(x) = sqrt(x) to the right by 2 units?

• f(x) = sqrt(x) + 2

• f(x) = sqrt(x + 2)

• f(x) = sqrt(x) - 2

• f(x) = sqrt(x - 2)

What is the effect of subtracting a constant inside the square root in the function f(x) = sqrt(x - c)?

• Shifts the graph up by c units

• Shifts the graph right by c units

• Shifts the graph left by c units

• Shifts the graph down by c units