Answer:
The transformed function is [tex]g(x) = 2\cdot f(x)[/tex], [tex]\forall\,x \in \mathbb{R}[/tex].
Step-by-step explanation:
Let be [tex]f(x)[/tex] and [tex]g(x)[/tex] continuous functions in x. In this case, the stretch factor consist on multiplying [tex]f(x)[/tex] by a scalar factor, so that:
[tex]g(x) = k \cdot f(x)[/tex], [tex]\forall\, k\in \mathbb{R}, k \neq 0[/tex]
The stretch factor is:
[tex]k = \frac{g(x)}{f(x)}[/tex], [tex]\forall\, x \in \mathbb{R}[/tex]
If [tex]f(-3) = -5[/tex] and [tex]g(-3) = -10[/tex], then:
[tex]k = \frac{g(-3)}{f(-3)}[/tex]
[tex]k = \frac{-10}{-5}[/tex]
[tex]k = 2[/tex]
The transformed function is [tex]g(x) = 2\cdot f(x)[/tex], [tex]\forall\,x \in \mathbb{R}[/tex].
