Vertical Translations of Functions

The video tutorial explains how to graph the function f(x) = 2x + 3 and explores the effects of translating the graph by adding or subtracting a constant K. It demonstrates how adding K shifts the graph up, while subtracting K shifts it down, without changing the slope. The tutorial provides examples of graphing f(x) + 2 and f(x) - 2, showing how each point on the graph is moved vertically by the value of K.

What is the initial function discussed in the video?

• f(x) = 2x - 3

• f(x) = 2x + 3

• f(x) = x^2 + 3

• f(x) = 3x + 2

What happens to the graph of f(x) when you add a positive constant?

• It shifts downwards.

• It shifts to the left.

• It shifts to the right.

• It shifts upwards.

If f(x) is translated upwards by 2 units, what is the new function?

• f(x) = 2x + 1

• f(x) = 2x + 2

• f(x) = 2x + 5

• f(x) = 2x + 3

How does the graph change when you subtract a constant from f(x)?

• It shifts upwards.

• It shifts to the right.

• It shifts to the left.

• It shifts downwards.

What is the effect of subtracting 2 from f(x) on the graph?

• The graph moves up by 2 units.

• The graph moves down by 2 units.

• The graph moves left by 2 units.

• The graph moves right by 2 units.

What does the constant k do to the graph of f(x)?

• It shifts the graph horizontally.

• It reflects the graph.

• It shifts the graph vertically.

• It changes the slope.

If k is negative, in which direction does the graph shift?

• Right

• Left

• Downwards

• Upwards

What remains unchanged when the graph is translated vertically?

• The y-intercept

• The x-intercept

• The curvature

• The slope

Which of the following is true about the slope during vertical translations?

• The slope becomes zero.

• The slope remains the same.

• The slope decreases.

• The slope increases.

What is the primary focus of the video regarding graph translation?

• Changing the slope

• Vertical shifts

• Reflecting the graph

• Horizontal shifts