Understanding Graph Transformations

The video tutorial explains how to graph functions and apply transformations such as scaling and shifting. It begins with an introduction to graphing a segment of f(x) = x and then explores how to graph h(x) = 1/3 * f(x) - 5 by scaling and shifting the original graph. The tutorial provides a step-by-step example of graphing f(x-3), demonstrating how subtracting a value from x shifts the graph to the right. It further explains how multiplying by -2 scales the graph and how adding a constant shifts it vertically. The tutorial concludes with a complete transformation of the function, illustrating the final graph of G(x) = -2 * f(x-3) + 4.

What is the initial function given in the problem?

• f(x) = x

• f(x) = x^2

• f(x) = 2x

• f(x) = x + 1

How does multiplying a function by a constant affect its graph?

• It shifts the graph vertically.

• It scales the graph vertically.

• It reflects the graph over the x-axis.

• It shifts the graph horizontally.

What is the effect of subtracting 5 from the function 1/3 f(x)?

• The graph shifts 5 units up.

• The graph shifts 5 units to the left.

• The graph shifts 5 units down.

• The graph shifts 5 units to the right.

What happens to the graph of a function when you subtract a constant from the input variable?

• The graph shifts to the left.

• The graph shifts to the right.

• The graph shifts downwards.

• The graph shifts upwards.

What is the result of multiplying a function by -2?

• The graph is shifted downwards.

• The graph is reflected over the y-axis.

• The graph is reflected over the x-axis.

• The graph is shifted upwards.

What is the purpose of creating a table in the transformation process?

• To track changes in the function values

• To determine the x-intercepts

• To find the y-intercepts

• To calculate the slope of the graph

What is the result of shifting a graph horizontally by 3 units?

• The graph moves 3 units up.

• The graph moves 3 units to the right.

• The graph moves 3 units to the left.

• The graph moves 3 units down.

How does adding 4 to the function g(x) affect its graph?

• The graph shifts 4 units up.

• The graph shifts 4 units to the left.

• The graph shifts 4 units to the right.

• The graph shifts 4 units down.

What is the final transformation applied to obtain g(x)?

• Scaling by -2 and shifting down by 4

• Scaling by 2 and shifting down by 4

• Scaling by -2 and shifting up by 4

• Scaling by 2 and shifting up by 4

What is the effect of a negative scaling factor on a graph?

• It reflects the graph over the x-axis.

• It shifts the graph to the left.

• It shifts the graph to the right.

• It reflects the graph over the y-axis.