Suppose that the \( x \)-intercepts of the graph of \( y=f(x) \) are -6 and -3. (a) What are the \( x \)-intercepts of the graph of \( y=f(x+8) \) ? The \( x \)-inlercepts of the graph of \( y=f(x+8) \) are \( -14,-11 \). (Use a comma to separate answers as needed.) (b) What are the \( x \)-intercepts of the graph of \( y=f(x-7) \) ? The \( x \)-intercepts of the graph of \( y=f(x-7) \) are 1,4 . (Use a comma to separate answers as needed.) (c) What are the \( x \)-intercepts of the graph of \( y=3 f(x) \) ? The \( x \)-intercepts of the graph of \( y=3 f(x) \) are \( \square \). (Use a comma to separate answers as needed)

If you multiply a function's output by a constant, like in \( y=3f(x) \), it doesn’t change the \( x \)-intercepts of the graph. The reason? The \( x \)-intercepts occur where \( f(x) = 0 \), which remains true regardless of how you stretch or compress the graph vertically. So, the \( x \)-intercepts for \( y=3f(x) \) remain the same as those of \( f(x) \): \(-6, -3\). Want to visualize this concept? Picture a rubber band stretched up and down while pinned at two points on a table. The points where the rubber band touches the table are your \( x \)-intercepts! Even if you change how high the band stretches, those two points where it touches the table are fixed. So, keep those \( x \)-intercepts as they are: \(-6, -3\)!