Ease Into Prep with an SAT^® Question of the Day

Difficulty:Hard

Category:Passport to Advanced Math / Functions

Strategic Advice:Think about how the transformations affect the graph ofg(x) and draw a sketch ofh(x) on the same grid. Compare the new graph to each of the answer choices until you find one that is true.

Getting to the Answer:The graph ofh(x) = –g(x) + 1is a vertical reflection ofg(x), over thex-axis, that is then shifted up 1 unit. The graph looks like the dashed line in the following graph:

Now, compare the dashed line to each of the answer choices: the range ofh(x) is the set ofy-values from lowest to highest (based on the dashed line). The lowest point occurs at pointB’ and has ay-value of –3; the highest value occurs at both ends of the graph and is 3, so the range is$-3\le y\le 3$. This means (A) is correct and you can move on to the next question. Don’t waste valuable time checking the other answer choices unless you are not sure about the range. (Choice B: The minimum value ofh(x) is –3, not –4. Choice C: The coordinates of pointAonh(x) are (–2, –2), not (2, 4). Choice D: the graph ofh(x) is decreasing, not increasing, betweenx= –5andx= –2.)