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melisa1 [442]
3 years ago
10

Which of the following accurately shows the range of the function defined below?

Mathematics
1 answer:
tangare [24]3 years ago
5 0

Answer:

[2, positive infinity)

Step-by-step explanation:

the range is the interval of possible y-values or f(x) values.

for x<0 y is always and only 3.

for x between 0 and 2, y = x² + 2.

it clearly increases with increasing x. so, what is y for the smallest x ? the smallest x here is 0.

y = 0² + 2 = 2

for x larger or equal to 2, y = (1/2)×x + 5.

it again increases with increasing x. the smallest x here is 2.

y = (1/2)×2 + 5 = 1 + 5 = 6.

so, the smallest possible value for y is 2. and then it will approach positive infinity, when x approaches positive infinity. but it can never reach that (only after infinite time and at infinite x, so it is officially undefined), so that the interval is open on that end.

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x\:>\:5+1

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QUESTION B.

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x \le \frac{6}{2}.

x \le 3.

Answer: 5. x \le 3, closed dot at 3 and shaded to the left(B).

QUESTION C

The given inequality is x-7\:>\:-4

Add 7 to both sides to get;

x\:>\:-4+7

\Rightarrow x\:>\:3

Answer: 7. x\:>\:3, open dot at 3 and shaded to the right.(C)

QUESTION D

We want to solve;

-2x \:

Divide through by -2 and reverse the inequality sign;

x \:>\:\frac{6}{-2}

x \:>\:-3

Answer; 3. x \:>\:-3 Open dot at -3 and shaded to the right. (D)

QUESTION E

We have  

4\:

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\frac{4}{-4}\:>\:x

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x\:

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The given inequality is -2x+3\:

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-2x\:

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The given  inequality is

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x\:

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