Graphing Transformations of Functions

The video tutorial explains the process of transforming graphs through horizontal shifts, stretching, shrinking, and vertical shifts. It uses the example of transforming f(x) = x^2 into g(x) = 2(x+3)^2 - 1, detailing each step in the transformation process. The tutorial emphasizes the importance of following a specific order when applying multiple transformations to achieve the desired graph.

What is the first step in the order of graph transformations?

• Vertical shift

• Horizontal shift

• Reflection

• Stretching and shrinking

When horizontally shifting a graph, what determines the direction of the shift?

• The slope of the graph

• The coefficient of x

• The constant added or subtracted inside the function

• The y-intercept

If a point (2, 4) is shifted three units to the left, what will be its new coordinates?

• (2, 1)

• (-1, 7)

• (-1, 4)

• (5, 4)

What does a multiplier of 2 in front of a function indicate?

• The graph will be reflected

• The graph will be stretched by a factor of 2

• The graph will be shifted down by 2 units

• The graph will be shifted up by 2 units

If a point (0, 4) is stretched by a factor of 2, what will be its new coordinates?

• (4, 0)

• (0, 2)

• (2, 4)

• (0, 8)

What is the effect of a negative sign outside the function on the graph?

• It reflects the graph

• It shifts the graph to the right

• It stretches the graph

• It shifts the graph to the left

In the given example, is there any reflection applied to the graph?

• Yes, about the y-axis

• Yes, about both axes

• Yes, about the x-axis

• No reflection is applied

What is the final step in the order of graph transformations?

• Reflection

• Vertical shift

• Stretching and shrinking

• Horizontal shift

If a point (0, 0) is shifted down by 1 unit, what will be its new coordinates?

• (0, -1)

• (0, 1)

• (-1, 0)

• (1, 0)

What is the final transformed function in the example?

• G(x) = x^2 + 3

• G(x) = 2(x + 3)^2 - 1

• G(x) = (x + 3)^2

• G(x) = 2(x - 3)^2 + 1