Question

Analyze the graph of the function f(x) to complete the statement.

Answer 1

f(x) is the same as y, so we can say y = f(x)

Writing f(x) < 0 means we want to find when y < 0.

Visually, we are looking at the graph when the curve is below the horizontal x axis.

This is the portion in red that I have marked in the diagram (see attached image below). I apologize for the numbers being blurry.

The left red portion is from negative infinity to -3. In terms of a compound inequality we write $-\infty < x < -3$ which in interval notation is $(-\infty, -3)$. The curved parenthesis tells the reader to exclude both endpoints.

The right red portion is from x = -1.1 to x = 0.9, excluding both endpoints. So we say $-1.1 < x < 0.9$ which becomes the interval notation $(-1.1, 0.9)$. This is not ordered pair notation even though it looks identical to it.

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Answer in interval notation:  $(-\infty, -3) \cup (-1.1, 0.9)$

The "U" means "set union" which glues together the two separate intervals. Basically it's saying "x is either in the interval (-infinity, -3) or it is in the interval (-1.1, 0.9)"