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

Answer:

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

Step-by-step 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:

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

The stretch factor is:

$k = \frac{g(x)}{f(x)}$, $\forall\, x \in \mathbb{R}$

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

$k = \frac{g(-3)}{f(-3)}$

$k = \frac{-10}{-5}$

$k = 2$

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