Question

what transformations does y=cos x undergo to produce y=-3 cos(x)+1?

Answer 1

What happens when you add a constant to a function? If I add + 2 for example, it shifts 2 units up, - 2 would make it go 2 units down. We also know that when we multiply the equation by a number, either a vertical stretch/horizontal compression takes place or a vertical compression/horizontal stretch takes place. And we know that whichever in this takes place is by a factor of the number being multiplied with.

Can you use this information to figure out what you would have to do first and last in order to figure out the graph of y = cos(x) as it is transformed? @gymgirl21

Answer 2

would it be a Horizontal compression by factor 3, vertical shift by 1 unit up, then a reflection through the x-axis

Answer 3

Since we know that the leading coefficient is negative, we know that it will be reflected in the x-axis. Since the values are then multiplied by a factor of 3, then the graph is stretched, meaning all of it's values are multiplied by 3. And then you shift the graph 1 unit up.

Does that make sense? @gymgirl21

Answer 4

yes thank you

Answer 5

No problem. Medal/fan? :D lol @gymgirl21