interactive: dynamic figure 2.49 consider the graph y = f(cx). for what values of c is the graph reflected…

interactive: dynamic figure 2.49 consider the graph y = f(cx). for what values of c is the graph reflected about the y - axis and then horizontally stretched? c < 0 0 < c < 1 0 < c < -1 c > 0 this dynamic figure shows the graph of y = f(x) and y = f(cx) for varying values of c. drag the movable point along the slider to change the values of c.

interactive: dynamic figure 2.49 consider the graph y = f(cx). for what values of c is the graph reflected about the y - axis and then horizontally stretched? c < 0 0 < c < 1 0 < c < -1 c > 0 this dynamic figure shows the graph of y = f(x) and y = f(cx) for varying values of c. drag the movable point along the slider to change the values of c.

Answer

Explanation:

Step1: Recall transformation rules

For $y = f(cx)$, a negative - value of $c$ reflects the graph of $y = f(x)$ about the $y$-axis. When $|c|\lt1$, the graph of $y = f(x)$ is horizontally stretched.

Step2: Analyze the conditions

We want a reflection about the $y$-axis (so $c\lt0$) and a horizontal stretch. If $c\lt0$ and $|c|\lt1$, then $ - 1\lt c\lt0$. But among the given options, the condition for reflection about the $y$-axis and horizontal stretch is met when $c\lt0$ because when $c\lt0$, reflection occurs and for some values of $c$ in this range, horizontal stretch also happens.

Answer:

$c < 0$