Question

The curve with equation y = f ( x ) is stretched so that the point (-3,-5) moves to the point (-3,-10). State in terms of f ( x ) the transformed function.

Answer 1

The transformed function is
`g(x) = 2\cdot f(x)`,
`\forall\,x \in \mathbb{R}`.

Explanation:

Let be
`f(x)` and
`g(x)` continuous functions in x. In this case, the stretch factor consist on multiplying
`f(x)` by a scalar factor, so that:

`g(x) = k \cdot f(x)`,
`\forall\, k\in \mathbb{R}, k \\eq 0`

The stretch factor is:

`k = (g(x))/(f(x))`,
`\forall\, x \in \mathbb{R}`

If
`f(-3) = -5` and
`g(-3) = -10`, then:

`k = (g(-3))/(f(-3))`

`k = (-10)/(-5)`

`k = 2`

The transformed function is
`g(x) = 2\cdot f(x)`,
`\forall\,x \in \mathbb{R}`.