Graph Transformations and Shifts

The video tutorial explains how to shift graphs using transformations. It covers how the values of c and d in the function g(x) = f(x + c) + d affect horizontal and vertical shifts. The tutorial provides examples of shifting graphs by translating endpoints and using arithmetic to calculate new coordinates. It concludes with a summary of the concepts discussed.

What does the parameter 'c' indicate in the transformation g(x) = f(x + c) + d?

• A shift up or down

• A shift left or right

• A reflection over the x-axis

• A change in the slope

If c is less than zero in the transformation g(x) = f(x + c) + d, which direction does the graph shift?

• Down

• Up

• Right

• Left

In the example g(x) = f(x - 5) + 4, what is the transformation applied to the graph?

• Shift left 5 units, up 4 units

• Shift right 5 units, down 4 units

• Shift left 5 units, down 4 units

• Shift right 5 units, up 4 units

How do you determine the new x-coordinate when shifting a point right by 5 units?

• Multiply the x-coordinate by 5

• Divide the x-coordinate by 5

• Add 5 to the x-coordinate

• Subtract 5 from the x-coordinate

What is the new y-coordinate if you shift a point up by 4 units?

• Divide the y-coordinate by 4

• Multiply the y-coordinate by 4

• Add 4 to the y-coordinate

• Subtract 4 from the y-coordinate

In the transformation g(x) = f(x + 2) - 3, what does the '+2' indicate?

• Shift up 2 units

• Shift left 2 units

• Shift down 2 units

• Shift right 2 units

What is the effect of '-3' in the transformation g(x) = f(x + 2) - 3?

• Shift up 3 units

• Shift down 3 units

• Shift left 3 units

• Shift right 3 units

If a graph is shifted left by 2 units and down by 3 units, what is the new position of the point (5, 2)?

• (7, 5)

• (3, -1)

• (7, -1)

• (3, 5)

What is the new position of the point (-2, 4) after shifting left 2 units and down 3 units?

• (-2, 7)

• (-2, 1)

• (-4, 7)

• (-4, 1)

What is the main takeaway from the video on graph transformations?

• Graph transformations are only vertical.

• Graph transformations can be both horizontal and vertical.

• Graph transformations are only horizontal.

• Graph transformations do not affect endpoints.