Question

What type of transformation occurs when we change the value of a?

Answer 1

When we change the value of "a" in a mathematical function, particularly in the form
`\(f(x) = a \cdot g(x)\)`, it represents a vertical stretch or compression transformation. If
`\(|a| > 1\),` it's a vertical stretch; if
`\(0 < |a| < 1\)`, it's a vertical compression.

Changing the value of "a" in a mathematical function, such as
`\(f(x) = a \cdot g(x)\)`, results in a vertical stretch or compression transformation. If the absolute value of "a" is greater than 1, it causes a vertical stretch, expanding the graph vertically.

Conversely, if the absolute value of "a" is between 0 and 1, it leads to a vertical compression, squeezing the graph vertically. This transformation alters the amplitude or height of the function, affecting how rapidly it oscillates or decays. Adjusting "a" allows for the manipulation of the vertical scale, providing flexibility in modeling and analyzing mathematical relationships.

The complete question is:
What type of transformation occurs when we change the value of A in mathematical function
`\(f(x) = a \cdot g(x)\)`?