# Does this graph represent a linear function?

a) Does this graph represent a linear function?

Since this function does not graph to a straight line like linear functions do, does that make it not represent a linear function?

b) What is happening to the tide at point c?

I'm assuming the tide is rolling out by looking at the way the point is marked on the graph.

c) Using set builder notation, state the domain and range of the graph.

Domain: $\{ x ~|~ x > 0,~ x \in \mathbb{R} \}$

Range: $\{ y ~|~ y < 30,~ y \in \mathbb{R} \}$

• It is difficult to read the diagram well due to its low resolution, but look at part (b) a bit closer. "What is happening to the tide at point $c$." Where was the tide recently before $c$? Where is it going shortly after $c$? Would that imply the tide is rising or falling? (I.e. is it positive or negative slope at $c$?) Aug 5, 2015 at 3:37

c) The domain should include $0$ and the range should be $\{y \: \:|\:5 \le y \le 30, y \in \mathbb{R} \}$
• It is arguable about whether or not the domain should extend to the left of zero as well. The fact that they appear to use an arrow on the far left of the graph implies that it may well continue in that direction. It is not inherently incorrect to think of the domain as being $\{x~|~0\leq x~,~x\in\mathbb{R}\}$ as that may have all the information needed for use, but it appears that the intended interpretation might be $\{x~|~x\in\mathbb{R}\}$ instead. The question is if anyone would be inclined to use this function to estimate the tide a few weeks ago. Aug 5, 2015 at 3:44