Graph Transformations and Properties

This video tutorial covers the transformations of graphs, focusing on vertical and horizontal translations, reflections, and complex transformations. It begins with basic transformations of the quadratic function y = x^2, explaining how adding or subtracting constants affects the graph's position. The tutorial then delves into horizontal shifts by altering input values and explores reflections over the x-axis and y-axis. The video also includes exam-style questions to apply these concepts and discusses the importance of the order of operations in complex transformations. Finally, it covers transforming functions and deriving new equations.

What is the basic shape of the graph y = x^2?

• A circle

• A straight line

• A hyperbola

• A parabola

If you add a constant to the function y = x^2, what happens to the graph?

• It remains unchanged

• It becomes a circle

• It shifts vertically

• It shifts horizontally

What is the effect of adding a constant inside the function's input, such as in y = (x + 2)^2?

• The graph shifts down

• The graph shifts left

• The graph shifts up

• The graph shifts right

Reflecting a graph in the x-axis involves which transformation?

• Multiplying the input by -1

• Adding a constant to the input

• Multiplying the function by -1

• Subtracting a constant from the output

In an exam question, if a graph is transformed by y = f(x) - 4, what is the transformation?

• Shift 4 units up

• Shift 4 units down

• Shift 4 units left

• Shift 4 units right