Question

given the graph of $y = f(x)$, shown as a red dashed curve, drag the green movable points to draw the graph of $y = f(-x)$. notice that you can control the positioning of the reflective function with the coordinate labeled \drag function\ and control the width of the reflection with the coordinate labeled \control width.\ provide your answer below:

Explanation:

Step1: Recall reflection over y-axis

The transformation \( y = f(-x) \) is a reflection of the graph of \( y = f(x) \) over the \( y \)-axis. For any point \( (x, y) \) on \( y = f(x) \), the corresponding point on \( y = f(-x) \) is \( (-x, y) \).

Step2: Apply to given graph

• The "Drag Function" point (let's say it has a coordinate \( (a, b) \) on \( y = f(x) \)) should be moved to \( (-a, b) \) for \( y = f(-x) \).
• The "Control Width" point (with coordinate \( (c, d) \) on \( y = f(x) \)) should be moved to \( (-c, d) \) for \( y = f(-x) \).

Looking at the graph, the red dashed curve is \( y = f(x) \). To draw \( y = f(-x) \), we reflect each point of the red curve over the \( y \)-axis. So the green points (Drag Function and Control Width) on the red curve should be mirrored across the \( y \)-axis. For example, if the Drag Function point is at \( (2, 3) \) (visually, around \( x = 2 \), \( y = 3 \)) on the red curve, it should move to \( (-2, 3) \), and the Control Width point (e.g., at \( (5, -1) \)) should move to \( (-5, -1) \), adjusting the curve to be the mirror image over the \( y \)-axis.

Answer:

To draw \( y = f(-x) \), reflect the graph of \( y = f(x) \) (red dashed curve) over the \( y \)-axis. Move the "Drag Function" and "Control Width" green points to their mirror - image positions across the \( y \)-axis. The resulting graph (green curve) should be the reflection of the red dashed curve over the \( y \)-axis, with the green points placed such that for each point \( (x,y) \) on the red curve, the corresponding point on the green curve is \( (-x,y) \).