Difficulty:Hard

Category:Passport to Advanced Math / Functions

Strategic Advice:Transformations that are grouped with thexin a function shift the graph horizontally and, therefore, affect thex-coordinates of points on the graph. Transformations that are not grouped with thexshift the graph vertically and, therefore, affect they-coordinates of points on the graph. Remember, horizontal shifts are always backward of what they look like.

Getting to the Answer:Start with(x+ 3). This shifts the graph left 3, so subtract 3 from thex-coordinate of the given point:(5, 1)→(5 – 3, 1) = (2, 1). Next, apply the negative in front off, which is not grouped with thex, so it makes they-coordinate negative:(2, 1)→(2, –1). Finally, – 2 is not grouped withx, so subtract 2 from they-coordinate:(2, –1 – 2)→(2, –3).