Understanding Graph Transformations

The video tutorial explains how to graph functions by shifting the graph of f(x) = x. It covers two examples: g(x) = f(x) - 4, which shifts the graph down by 4 units, and h(x) = f(x + 6), which shifts the graph 6 units to the left. The tutorial emphasizes understanding how changes in the function's equation affect the graph's position.

What is the effect of defining g(x) as f(x) - 4 on the graph of f(x)?

• The graph shifts right by 4 units.

• The graph shifts left by 4 units.

• The graph shifts down by 4 units.

• The graph shifts up by 4 units.

If f(3) = 3, what is g(3) when g(x) = f(x) - 4?

• -1

• -7

• 3

• 7

How does the graph of g(x) = f(x) - 4 compare to the graph of f(x)?

• It is shifted left by 4 units.

• It is shifted right by 4 units.

• It is shifted down by 4 units.

• It is shifted up by 4 units.

If f(-3) = -3, what is g(-3) when g(x) = f(x) - 4?

• 1

• -3

• 3

• -7

What is the new function h(x) if h(x) = f(x + 6)?

• The graph shifts up by 6 units.

• The graph shifts left by 6 units.

• The graph shifts right by 6 units.

• The graph shifts down by 6 units.

If h(x) = f(x + 6), what happens to the graph of f(x)?

• It shifts right by 6 units.

• It shifts down by 6 units.

• It shifts left by 6 units.

• It shifts up by 6 units.

What is the value of h(8) if h(x) = f(x + 6) and f(-2) = -2?

• 2

• 0

• -2

• 8

What happens to the graph of f(x) when you replace x with x + 6?

• It shifts up by 6 units.

• It shifts down by 6 units.

• It shifts right by 6 units.

• It shifts left by 6 units.

If f(2) = 2, what is h(-4) when h(x) = f(x + 6)?

• -4

• 6

• 2

• 0

What is the effect of adding 6 to the x-value in the function h(x) = f(x + 6)?

• The graph shifts right by 6 units.

• The graph shifts left by 6 units.

• The graph shifts down by 6 units.

• The graph shifts up by 6 units.