Vertical Scaling of Functions: Key Concepts and Examples

The video tutorial explains how to graph function g(x) as a scaled version of function f(x). It covers examples where g(x) is defined as 1/3 f(x) and 2f(x), demonstrating how these transformations affect the graph's appearance. The tutorial uses tables and reference points to illustrate the changes, emphasizing the concepts of vertical scaling and stretching.

What is the initial transformation applied to function f to obtain function g?

• Scaling horizontally by 1/3

• Scaling vertically by 3

• Scaling vertically by 1/3

• Scaling horizontally by 3

If f(3) = -3, what is g(3) when g(x) = 1/3 f(x)?

• -1

• -3

• 3

• 1

What happens to the graph of g compared to f when g(x) = 1/3 f(x)?

• It remains unchanged

• It compresses vertically

• It stretches vertically

• It shifts horizontally

What is the new transformation applied to function f to obtain function g in the second example?

• Scaling horizontally by 2

• Scaling vertically by 2

• Scaling horizontally by 1/2

• Scaling vertically by 1/2

If f(0) = 1, what is g(0) when g(x) = 2 f(x)?

• -2

• 2

• 0

• 1

What is the effect on the graph of g compared to f when g(x) = 2 f(x)?

• It stretches vertically

• It compresses vertically

• It shifts horizontally

• It remains unchanged

In the final example, what is the transformation applied to function f to obtain function g?

• Scaling horizontally by 1/3

• Scaling vertically by 1/3

• Scaling vertically by 3

• Scaling horizontally by 3

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

• -3

• -9

• 3

• 9

What is the relationship between f and g when g(x) = 3 f(x)?

• g is 1/3 of f

• g is 3 times f

• g is the same as f

• g is the reciprocal of f

If f(0) = -2, what is g(0) when g(x) = 3 f(x)?

• -2

• 6

• 2

• -6