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Halp for a cookie :) ♥ ♥❣ ❣
*Piece-Wise Defined Functions*

Halp for a cookie :) ♥ ♥❣ ❣ *Piece-Wise Defined Functions*-example-1
User Spenhouet
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2 Answers

4 votes

Answer:


\textsf{A.} \quad \begin{cases}-x -2 \quad \text{if}\;x < -2\\x + 4 \quad \;\;\;\text{if}\;x \geq -2\end{cases}

Explanation:

When graphing piece-wise functions:

  • An open circle indicates the value is not included in the interval.
  • A closed circle indicates the value is included in the interval.
  • An arrow show that the function continues indefinitely in that direction.

From inspection of the given graph:

  • The equation for the line on the left side of the function has a negative slope and an x-intercept at x = -2.
  • There is an open circle at x = -2 and the line continues to the left.
    ⇒ x < -2

  • The equation for the line on the right side of the function has a positive slope and a y-intercept at y = 4.
  • There is a closed circle at x = -2 and the line continues to the right.
    ⇒ x ≥ -2

Therefore, the definition of the function is:


\begin{cases}-x + a \quad \text{if}\;x < -2\\x + 4 \quad \;\;\;\text{if}\;x \geq -2\end{cases}

where a is some constant.

The only answer option that matches the given parameters is option A.

User Genjuro
by
3.2k points
4 votes


{ \qquad\qquad\huge\underline{{\sf Answer}}}

The function shown in the graph above is a discontinuous function, at x = -2

For values of x less than -2, the left side of the graph is applicable. whose equation is :


\qquad \sf&nbsp; \dashrightarrow \: y - 0 = \cfrac{1 - 0}{ - 3 - ( - 2)} (x - ( - 2))


\qquad \sf&nbsp; \dashrightarrow \: y = \cfrac{1}{ - 3 + 2} (x + 2)


\qquad \sf&nbsp; \dashrightarrow \: y = - 1(x + 2)


\qquad \sf&nbsp; \dashrightarrow \: y = - x - 2 \:\: ; \:\:x<-2

For values of x greater than -2, the right side of the graph is applicable. whose equation is :


\qquad \sf&nbsp; \dashrightarrow \: y - 4= \cfrac{4 - 2 }{0 - (-2)} (x -0)


\qquad \sf&nbsp; \dashrightarrow \: y - 4 = \cfrac{2}{2} (x)


\qquad \sf&nbsp; \dashrightarrow \: y - 4 = x


\qquad \sf&nbsp; \dashrightarrow \: y = x + 4 \: \: ;\: \: x > - 2

So, the correct choice will be Option " A "

User Masoud Ramezani
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3.5k points