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d1i1m1o1n [39]
3 years ago
10

The graph represents the piecewise function...

Mathematics
1 answer:
Alexxx [7]3 years ago
7 0

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.

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What value or values of x satisfy 2x + 5.31 = 4.2?
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Answer:  x can equal -3.2 or -7.4.

Step-by-step explanation:

The correct expression is:

2|x+5.3|=4.2

So, we have an absolute value equation, where it can be positive or negative:

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2 (x+5.3)=4.2

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2[-(x+5.3)]=4.2

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x can equal -3.2 or -7.4.

Feel free to ask for more if needed or if you did not understand something.  

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