Start by plugging in what you know into the function given. If f(x) = x² – 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.

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 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).

On this question you can use Plugging In the Answers. The numbers in the answer choices replace the f(x) portion of the equation, so you can just write out the rest of it, ​\( \sqrt[]{3x-2} \)​, next to each to see if it can be true. Start with (A) since you are looking for the smallest value of f(x). If 0 = ​\( \sqrt[]{3x-2} \)​, then 0 = 3x – 2 when you square both sides. Add 2 to both sides to get 2 = 3x, and then divide both sides by 3. You get x = ​\( \frac{2}{3} \)​. Since this is a real value, the equation works, so the smallest value of f(x) is 0. Choice (A) is correct.