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loris [4]
2 years ago
5

Find the domain and the range of the relation shown on the

Mathematics
1 answer:
nika2105 [10]2 years ago
3 0

Answer:

Domain = {0.-6}

Range = {-2, 4}  

Notes We find coordinates and radius and state

Then we show formula  (x -x1)^2 + (y +y1) = r ^2 and show

(x -3 )^2 + (y − 1)^2 = 9 = R^2  THE RADIUS^2

then ;

Domain formula = x - r   and x + r

Range formula = y - r  and  y + r

Step-by-step explanation:

The graph is a circle so all the points are enclosed in it

The domain is the values for x so you subtract the radius from the centre coordinate and you add the radius to it The range is the values for y so you do the same to the y coordinate If you use

(x- x1) ^2 + (y - y1) ^2

(x -3 )^2 + (y − 1)^2 = 9

However this changes if centre coordinate shows negatives

we change negative x or y to + positive in the formula in bold.

Centre coordinate = (3.,1) radius is 3  SO = MUST BE THE RADIUS ^2

= (x - 3)^2 + (y - 1)^2 = 3^2  = 9  

Domain formula = x - r   and x + r

Domain  = 3 - 3 = 0

and - 3 + 3 = -6

Domain = {0.-6}

Range formula = y - r  and  y + r

Range = 1 - 3 = -2

and  1 +3 = 4

Range = {-2, 4}  

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Digiron [165]

QUESTION A

The given inequality is  

x-1\:>\:5

Add 1 to both sides of the inequality to obtain;

x\:>\:5+1

x\:>\:6

Answer: 2. x\:>\:6, open dot at 6 and shaded to the right.(A)

QUESTION B.

The given inequality is 2x \le 6.

Divide both sides by 2;

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\:

Divide through by -4 and reverse the sign.

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

-1\:>\:x

or

x\:

Answer: 6. x\: open dot at -1, and shaded to the left(E)

QUESTION F

The given inequality is -2x+3\:

Add -3 to both sides to get;

-2x\:

-2x\:

Divide both sides of the inequality by -2 and reverse the sign;

x\:>\:5

Answer:9. x\:>\:5, open dot at 5 and shaded to the right(F)

QUESTION G

The given  inequality is

5x+1\ge11

5x\ge11-1

5x\ge10

Divide by 5

x\ge2

Answer ; 10. x\ge2, closed dot at 2 and shaded to the right(G)

QUESTION H

We have 3(x+4)\:>\:8x-6

Expand the bracket to get;

3x+12\:>\:8x-6

Group similar terms to get;

3x-8x\:>\:-6-12

Simplify

-5x\:>\:-18

Divide through by -5 and reverse the sign;

x\:

Answer: 1. x\: Open dot at 18/5 and shaded to the left(H)

QUESTION I

We have -3x+4\:.

-3x+x\:

-2x\:

Divide by -2 and reverse the sign;

x\:>\:1

Answer: 8. x\:>\:1, open dot at 1 and shaded  to the right(I)

J. The given inequality -2(x-4)\:>\:5-(x+2)

Expand the bracket to get;

-2x+8\:>\:5-x-2

Group like terms to get;

-2x+x\:>\:5-2-8

-x\:>\:-5

Divide by -1 and reverse the sign to get;

x\:

Answer; 4. x\:, open dot at 5 and shaded to the left.(J)

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3 years ago
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