Question

PLS HELP me with math

Answer 1

c

Explanation:

A piecewise-defined function is properly graphed when the pieces of the definition match the pieces of the graph. To identify the function, match the pieces of the function with the pieces of the graph.

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domain pieces

The domain is the horizontal extent of the graph. The discontinuity in the graph at x=2 tells you the domain of the function will be divided into 2 parts.

The solid dot on the part of the graph that extends to the left tells you that x=2 and points to its left are one part of the domain: x ≤ 2.

The open dot on the part of the graph that extends to the right tells you that x=2 is not part of the domain for that section. It will be x > 2.

Recognizing that these are the domain definitions already eliminates choices B and D.

function definitions

The answer choices (or your examination of the graph) tell you that the two lines are described by ...

• y = x+2
• y = x+1

The y-intercept for the line to the left of x=2 is clearly at y=2, so we now know the match-up between domains and function definitions is ...

`y=\begin{cases}x+2&x\le2\\x+1&x > 2\end{cases}`

This eliminates choice A.

The correct answer choice is C:

`\boxed{\textsf{c.}\quad y=\begin{cases}x+1&x > 2\\x+2&x\le2\end{cases}}`