Understanding Function Transformations

The video tutorial covers function transformations, including vertical and horizontal shifts, reflections, and stretches. It provides examples of graphing functions like x squared, absolute value, and square root functions, demonstrating how to apply transformations. The tutorial also explains how to identify the direction of shifts and the effects of negative signs on graphs. Techniques for graphing using parent functions are discussed, along with advanced examples to solidify understanding.

What type of transformation occurs when a constant is added to a function f(x)?

• Reflection over x-axis

• Vertical shift

• Reflection over y-axis

• Horizontal shift

If f(x) is transformed to f(x - 4), in which direction does the graph shift?

• 4 units to the right

• 4 units down

• 4 units to the left

• 4 units up

How does the graph of y = |x + 2| differ from the parent function y = |x|?

• Shifts 2 units down

• Shifts 2 units to the left

• Shifts 2 units up

• Shifts 2 units to the right

What is the effect of multiplying a function by a fraction less than 1?

• Vertical stretch

• Horizontal stretch

• Vertical shrink

• Horizontal shrink

Which quadrant does the graph of y = -√(-x) move towards?

• Quadrant 2

• Quadrant 3

• Quadrant 4

• Quadrant 1

What is the parent function of y = x^3?

• y = √x

• y = x^3

• y = x^2

• y = x

How does the graph of y = (x - 2)^2 + 3 differ from y = x^2?

• Shifts 2 units left and 3 units up

• Shifts 2 units right and 3 units up

• Shifts 2 units right and 3 units down

• Shifts 2 units left and 3 units down

What is the vertex of the parabola y = 3 - (x + 2)^2?

• (-2, 3)

• (2, 3)

• (2, -3)

• (-2, -3)

In the function y = 4 - √(3 - x), what does the negative sign in front of the square root indicate?

• Reflection over y-axis

• Vertical shift

• Horizontal shift

• Reflection over x-axis

What is the effect of a negative sign inside the function, such as in y = √(-x)?

• Reflects over the x-axis

• Reflects over the y-axis

• Reflects over the origin

• No reflection