Question

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Answer 1

Answer:

The complete graph of $f\left(x\right)=\left\{-2x:x\ge 3,\:y=-\frac{1}{3}x-5:x\le \:3\right\}$ is shown below.

Step-by-step explanation:

Considering the function

$f\left(x\right)=\left\{-2x:x\ge 3,\:y=-\frac{1}{3}x-5:x\le \:3\right\}$

The graph of the piece $y=-2x\ \ \ \ \ \left\{x\ge3\right\}$ indicates the blue line, starting at x=3. And with one unit increase in x, the value of y decreases by 2 units.

For example,

at x = 3

$y = -2x$

$= -2(3)$

 $= 6$

and

at x = 4

$y = -2x$

  $= -2(4)$

  $= 8$

By comparing the slope intercept form

$y=mx+b$

Here,

The slope of which is m = -2,

and the piece $y=-\frac{1}{3}x-5\ \ \ \ \ \left\{x\le3\right\}$ indicates the yellow line.

By comparing the slope intercept form

$y=mx+b$

Here,

• The slope of which is m = -1/3, and

• y - intercept = -5.

The complete graph of $f\left(x\right)=\left\{-2x:x\ge 3,\:y=-\frac{1}{3}x-5:x\le \:3\right\}$ is shown below.