The graph below shows a function $y = f(x)\text{,}$ together with four fixed points on the graph. Also shown are four free points for you to click and drag to other locations. Suppose we wanted to compress the graph of $f$ horizontally toward the $y$–axis, so that each point on the curve was exactly half its current distance from the $y$–axis. Move the four free points to show where the fixed points would be if they were compressed toward the $y$–axis. If you place them correctly, a complete, compressed graph will appear. Did you correctly place the points? Answer: ? yes no There was one point on the graph of $f$ that did not move when the graph was compressed. Which point was it? ? the x-intercepts the y-intercept The graph above shows the same function $f$ as before. This time, you can use a slider to graph a transformation of the form $$y = f(ax)$$ where $a$ is a constant number. Notice that the formula for the transformation is shown using function notation. Use the slider until the transformed graph is exactly half as wide as the original graph of $f\text{.}$ Then use function notation to write the formula for the transformation. Answer: $y =$