Question

Which of the following functions is graphed below?

Answer 1

Option C

Explanation:

Let's work backwards.

Your second function is a line starting with a closed circle at x = 4. The line has an interval (4, ∞). Because of the previously mentioned closed circle, you are to include x = 4 in this part of the piece-wise equation. This changes your interval to [4, ∞) OR x ≥ 4. Just from that alone, you can determine that option C is your answer. But let's continue to the quadratic.

If the line covers [4, ∞) or x ≥ 4, that means the quadratic covers the remainder. However, it cannot also be set equal to 4 not only because it's already taken by the second function, but because it ends with an open circle at x = 4. That open circle is your indication that you cannot include it in that part of the piece-wise equation. The quadratic covers (-∞, 4) or x < 4.

With this, you should have x < 4 following the quadratic and x ≥ 4 following the line. The answer that includes both of these features is option C.

Answer 2

C.

Explanation:

The graph is a parabola when x < 4, so A and B are wrong.

The open circle indicates that (4, 19) is not included in the left half of the function.

The closed circle indicates that (4, 8) is included in the right half of the function.

Option C is correct.