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iwantcandy2002

04.01.2020

Mathematics

Option B: $f(x)=\left\{\begin{array}{l} x+3, \ \ x<0\\\\3, x\geq 0\end$ is the function

Explanation:

Given that the function has 2 connecting lines.

The first line goes from (-5,-2) to (0,3)

The second line starts at (0,3) and continues horizontally at y=3

Now, we need to determine the function.

Let us determine the function for the first line.

The coordinates are (-5,-2) and (0,3)

The slope of the first line is given by

$m=\frac{y_2-y_1}{x_2-x_1}$

Substituting the coordinates, we have,

$m=\frac{3+2}{0+5}$

$=\frac{5}{5}$

Thus, slope is m=1 and y - intercept is b=3

Substituting the slope and y - intercept in the slope - intercept formula, we have,

y=mx+b

y=x+3

Hence, the function of the first line is y=x+3

Now, we shall find the function of the second line.

It is given that the line continues horizontally at y=3

Thus, the function of the second line is y=3

Therefore, the function of the graph is given by

$f(x)=\left\{\begin{array}{l} x+3, \ \ x<0\\\\3, x\geq 0\end$

Hence, Option B is the correct answer.

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