The graph of the piecewise function is shown.

Mathematics

2 answers:

Lelechka [254]3 years ago

8 0

{ f(x)| –∞ < f(x) ≤ 4}

Sliva [168]3 years ago

7 0

b){ f(x)| –∞ < f(x) ≤ 4}

Hope it helps!

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--------------------------------------------------------------------------
Equation
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$y - 9 = - \dfrac{1}{2} (x + 2)$

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Rearrange the equation
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$y - 9 = - \dfrac{1}{2} (x + 2) \\ \\
 y - 9 = - \dfrac{1}{2}x - 1 \\ \\
 y - 9 + 9 = - \dfrac{1}{2}x - 1 + 9 \ \Longleftarrow \text{add 9 to both side} \\ \\
 y = -\dfrac{1}{2}x + 8$

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slope of the perpendicular line
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slope = 2

(*the slope of the perpendicular line is the negative reciprocal of the slope of line)

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Substitute slope into equation y = mx + c
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y = 2x + c

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Find y-intercept
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y = 2x + c
At point (0, 4)
4 = 2(0) + c
c = 4

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Substitute y-intercept into the equation y = 2x + c
-----------------------------------------------------------------------------
y = 2x + 4

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Answer: y = 2x + 4
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