respectively. Choices (B) and (D) result when the distance formula is not used. If you have
trouble remembering the distance formula, sketch a figure, and use the Pythagorean theorem
as detailed in the introductory chapter.
41 . C The correct answer is (C). There are two good ways to solve this question. Even if you don’t
know anything about absolute value questions, you can still get this right by plugging the
given point into the answer choices. Here’s what you get:
A.−3 = |−2 + 2| + 3, which simplifies to −3 = 3. Incorrect.
B.−3 = |−2 − 2| − 3, which simplifies to −3 = 1. Incorrect.
C.−3 = |−2 + 2| − 3, which simplifies to −3 = −3. Correct.
D.−3 = |−2 + 3| − 2, which simplifies to −3 = −1. Incorrect.
E.−3 = |−2 − 3| + 3, which simplifies to −3 = 7. Incorrect.
A slightly faster way to do this question is to memorize the basic form of an absolute value
equation. For the equation y = |x − a| + b, the vertex is (a, b). Plugging the vertex (−2,−3)
into this formula gives us y = |x − (−2)| − 3, which simplifies to y = |x + 2| − 3.
47 . C This question is best done with POE and a little bit of ballparking. First, deal with the y-
intercept. Since the line crosses the y-axis below the origin, the y-intercept must be negative,
so eliminate (B) and (D). Next, deal with the sign of the slope. A line that slopes down from
left to right has a negative slope, so eliminate (E). Finally, decide whether the numerator is
more or less than the denominator. Remember, slope is rise over run. The total run of this line
(distance from left to right) is 10, but the rise is considerably less than that, so the numerator
must be less than the denominator. Eliminate (A), leaving only (C).
48 . J For any function f(x + h) + k, h indicates horizontal shifts, and k indicates vertical shifts.
Because the horizontal shift is 4, not 3, you can eliminate (H). A negative h indicates a shift
right, not left, eliminating (F) and (G). A negative k indicates a shift down, not up,
eliminating (K).
50 . K The standard equation for a circle is (x − h)^2 + (y − k)^2 = r^2 , where the center of the circle is
the point (h,k). Therefore, the center of this circle is at the point (−3,5), which makes (K) the
correct answer.
56 . G The balloon remains stationary in the middle stage, so action (I) should be second in the
order of events, eliminating (F). In the first stage, the graph is increasing, which means the
distance between the balloon and the ground increases, so the balloon is moving away,
eliminating (H) and (K). The rate of increase is greater than the rate of decrease in the third
stage, so (J) is incorrect. Only (G) gives the correct actions in the correct order.
