CHAPTER DRILL ANSWERS AND EXPLANATIONS
Functions and Graphs Drill 1: No Calculator Section
3. B Start by plugging in what you know into the function given. If f(x) = x^2 – c, and f(–2) = 6, then
plug in –2 for x in the function: f(–2) = (–2)^2 – c. Solve and replace f(–2) with 6: 6 = 4 – c; 2 =
- c; and c = –2. If you picked (A), you forgot that (–2)^2 is positive 4.
7. A Try plugging in some values for x and see if the graphs include that point. If x = 0, then y = 0, so
(0, 0) should be a point on the graph. Unfortunately this doesn’t eliminate anything. If x = 1, then
y = 2, so (1, 2) should be a point on the graph. Eliminate (B), (C), and (D). The correct answer
is (A).
10. D First, find the slope of line l by using the slope formula: = 3. Plug this
slope and one of the points on line l into the slope-intercept form y = mx + b to solve for b,
giving you the full equation of the line. If you use the point (2, 5), you get 5 = 3(2) + b or 5 = 6
+ b, so b = −1. Therefore, the equation for line l is y = 3x − 1. For line m, the slope is given as
−2, and the x-intercept is 2. Be very careful not to jump to the conclusion that the equation of
line m is y = −2x + 2! In the form y = mx + b, the b is the y-intercept, not the x-intercept. The x-
intercept is where y = 0, so you know that (2, 0) is a point on line m. Use this point and the
slope to find the equation of line m in the same way you did for line l. 0 = −2(2) + b, so b = 4
and the equation is y = −2x + 4. Now set the x parts of the equations equal to find the point of
intersection. If 3x − 1 = −2x + 4, then 5x = 5 and x = 1. Again, be careful! The question asked
for the value of y ! Plug x = 1 into one of the line equations to find y. For line l, the equation
becomes y = 3(1) – 1 = 3 – 1 = 2, which is (D).
15. B The second graph moves down 1 and to the left 1. Remember that when a graph moves to the
left, it is represented by (x + h), which would be the same as x − (–1). So h = –1. Because a
negative k represents moving down, k = 1. Therefore, hk = (–1) × (1) = –1, and the correct
answer is (B).
Functions and Graphs Drill 2: Calculator-Permitted Section
6. A On this question you can use Plugging In the Answers. The numbers in the answer choices
