use the given function f to sketch the graph of the indicated transformation of f. click on segment…

Explanation:

Step1: Recall vertical - stretch rule

For a function $y = f(x)$, the transformation $y = a\cdot f(x)$ where $a>1$ (in this case $a = 2$) is a vertical stretch by a factor of $a$. Each $y$-coordinate of the points on the graph of $y = f(x)$ is multiplied by $a$.

Step2: Identify key points on $f(x)$

Let's assume some key points on the graph of $y = f(x)$. For example, if we have a point $(x_1,y_1)$ on $y = f(x)$.

Step3: Transform key points

For the transformation $y = 2\cdot f(x)$, the new point will be $(x_1,2y_1)$. For instance, if a point on $f(x)$ is $(- 3,-1)$, for $2\cdot f(x)$ the point will be $(-3,-2)$; if a point on $f(x)$ is $(3,1)$, for $2\cdot f(x)$ the point will be $(3,2)$.

Step4: Sketch the new graph

Connect the transformed key - points to sketch the graph of $y = 2\cdot f(x)$.

Answer:

Sketch the graph by multiplying the $y$-coordinates of the points on the original graph of $f(x)$ by 2 and then connecting the new points.