Question

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Answer 1

Answer:

D) -3

Step-by-step explanation:

we are given that f(x) = k has 3 real solutions.

Recall that graphically, this simply means that if we draw a  horizontal line y = k, the line will intersect the graph as 3 distinct locations.

Looking at the graph below (see attached picture for clarity), we can see that the only place where any horizontal line y = k will intersect the graph at 3 distinct points is between the blue lines pictured. (i.e approximately between y = -4 and y = -2.5)

If we look at all the choices, the only value for k  that falls between the blue lines is -3 (answer D). All the other values for y fall out outside the blue lines and hence do not satisfy the condition of having 3 real solutions

Answer 2

Answer: D)  -3

Explanation:

Recall that y = f(x) since both are outputs of a function.

If k = 2, then f(x) = 2 leads to y = 2 being a horizontal line drawn through 2 on the y axis. This horizontal line only crosses the cubic curve at one spot. The same can be said if k = 0 and k = -2. So we can rule out choices A,B,C.

On the other hand, if k = -3, then f(x) = -3 has three different solutions. This is because the horizontal line through -3 on the y axis crosses the cubic at 3 different intersection points.