Question

Please help!! I don't understand this!

Answer 1

Answer: The first one is "translated 4 units down". The second one is "vertically stretched by a factor of 4".

Recall that y = f(x). When we say f(x)-4, we really mean y-4 so that means each y coordinate of all the points on the graph have been reduced by 4. Visually this shifts the graph down 4 units. A translation in geometry is the technical term for shifting.

When we say 4*f(x), we are multiplying each y coordinate by 4. A point like (1,2) turns into (1,8) for instance. If you apply this to every point on the graph, then the curve is stretched vertically to be 4 times taller than it usually is; which is an informal way of saying "vertically stretched by a factor of 4"