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Vadim26 [7]
3 years ago
10

Question 14 Math Help please

Mathematics
1 answer:
Dmitry_Shevchenko [17]3 years ago
4 0

ANSWER

(1,0) is a solution

EXPLANATION

The given inequality is

y \leqslant |x + 2|- 3

We substitute the point to see which ones satisfy the inequality.

For (1,0)

0\leqslant|1+ 2|- 3

0\leqslant 0

This is true.

(1,0) is a solution.

For (-1-1)

- 1\leqslant | - 1 + 2|-3

- 1\leqslant-2

False

(-1,-1) is not a solution.

For (0,0)

0\leqslant|0+2|-3

0\leqslant- 1

False.

For (0,1)

1\leqslant|0+ 2|-3

1\leqslant-1

This is also false

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Answer:

Step-by-step explanation:

1). For a point (0, -15),

   Here x = 0, so the piece of function that applies,

   f(x) = 4x - 15 (Since, x = 0 lies in the range  -2 ≤ x < 4)

         = 4(0) - 15

         = -15

   True.

2). Since, f(x) = -\frac{1}{4}x^{2}+6x+36 for x < -2

                     = 4x - 15 for -2 ≤ x < 4

    Which shows a gap between these graphs.

    Therefore, graph has a discontinuity at x = -2

    True.

3). For x > 4,

   f(x) = 3^{x-4}

   For every input value of x in the interval (4, ∞), output values of the function will be increasing.

  So this option is TRUE.

4). In the interval (-12, -2),

   Function to be followed → f(x) = -\frac{1}{4}x^{2}+6x+36

   Graph of the given quadratic function opens downwards (Since, coefficient of x² is negative).

   In this graph value of function first increases then decreases.

   So the answer is FALSE.

5). Since, input values of the function 'f' varies from (-∞, ∞)

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   TRUE.    

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Step-by-step explanation:

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Answer:

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Step-by-step explanation:

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