Question

The graph represents the piecewise function...

Answer 1

Answer:

$f(x)=\left \{ {{2x-1,if\:x\le -1} \atop {x+4,if\:x\ge1}} \right.$

Step-by-step explanation:

We need to find the equation of the straight line on the interval $x\le -1$

This line passes through (-1,-3) and has slope 2.

The equation of this line is

$y+3=2(x+1)$

$\Rightarrow y+3=2x+2$

$\Rightarrow y=2x+2-3$

$\Rightarrow y=2x-1$

On the interval $x\ge 1$, the function is a straight line.

The straight line passes through; (1,5) and has slope 1.

The equation of this line is

$y-5=1(x-1)$

$\Rightarrow y-5=x-1$

$\Rightarrow y=x-1+5$

$\Rightarrow y=x+4$

The piece-wise function is;

$f(x)=\left \{ {{2x-1,if\:x\le -1} \atop {x+4,if\:x\ge1}} \right.$