Function Transformations and Graphing Techniques

The video tutorial explains how to determine the horizontal and vertical shifts of a function graph using function notation. It focuses on a specific SAT math question about shifting a function right by three units. The tutorial reviews the concepts of horizontal and vertical shifts, provides a solution to the problem, and verifies the solution using a graphing calculator. Additional examples are provided to reinforce the concepts.

What is the main focus of the SAT math question discussed in the video?

• Solving quadratic equations

• Calculating the area under a curve

• Shifting a function right by three units

• Finding the derivative of a function

In function notation, what happens when you add a constant to the input variable?

• The graph shifts right

• The graph shifts left

• The graph shifts up

• The graph shifts down

How does subtracting a constant from the input variable affect the graph?

• It shifts the graph left

• It shifts the graph right

• It stretches the graph horizontally

• It compresses the graph vertically

What is the effect of adding a constant outside the function in function notation?

• The graph shifts left

• The graph shifts right

• The graph shifts up

• The graph shifts down

What happens to the graph when a constant is subtracted from the function value?

• The graph shifts left

• The graph shifts right

• The graph shifts down

• The graph shifts up

Which function form represents a shift to the right by three units?

• f(x - 3)

• f(x) + 3

• f(x) - 3

• f(x + 3)

How can a graphing calculator be used to verify function shifts?

• By calculating derivatives

• By solving equations

• By entering the function and observing the graph

• By finding the area under the curve

What is the effect of a vertical compression on a graph?

• The graph becomes narrower

• The graph shifts down

• The graph becomes wider

• The graph shifts up

What transformation occurs when you multiply the function by a fraction?

• Vertical compression

• No transformation

• Horizontal shift

• Vertical stretch

What is the purpose of using a graphing calculator in function translation?

• To find the slope of a tangent

• To solve algebraic equations

• To verify the direction and magnitude of shifts

• To calculate integrals