QuestionDetermine if each equation defines y as a function of $x$ : 11. $x+y=16$ , 12. $x+y=25$ , 13. $x^{2}+y=16$ , 14. $x^{2}+y=25$ , 15. $x^{2}+y^{2}=16$ , 16. $x^{2}+y^{2}=25$ , 17. $x=y^{2}$ , 18. $4 x=y^{2}$ .

Studdy Solution

STEP 1

Assumptions1. An equation defines y as a function of x if for every value of x, there is exactly one corresponding value of y. . The equations are given in the form of $x$ and $y$ .

STEP 2

For the equation $x+y=16$ , we can express $y$ as a function of $x$ by isolating $y$ .
$y =16 - x$

STEP 3

In the equation $y =16 - x$ , for each value of $x$ , there is exactly one corresponding value of $y$ . Hence, this equation defines $y$ as a function of $x$ .

STEP 4

For the equation $x+y=25$ , we can express $y$ as a function of $x$ by isolating $y$ .
$y =25 - x$

STEP 5

In the equation $y =25 - x$ , for each value of $x$ , there is exactly one corresponding value of $y$ . Hence, this equation defines $y$ as a function of $x$ .

STEP 6

For the equation $x^{2}+y=16$ , we can express $y$ as a function of $x$ by isolating $y$ .
$y =16 - x^{2}$

STEP 7

In the equation $y =16 - x^{2}$ , for each value of $x$ , there is exactly one corresponding value of $y$ . Hence, this equation defines $y$ as a function of $x$ .

STEP 8

For the equation $x^{2}+y=25$ , we can express $y$ as a function of $x$ by isolating $y$ .
$y =25 - x^{2}$

STEP 9

In the equation $y =25 - x^{2}$ , for each value of $x$ , there is exactly one corresponding value of $y$ . Hence, this equation defines $y$ as a function of $x$ .

STEP 10

For the equation $x^{2}+y^{2}=16$ , we cannot express $y$ as a function of $x$ by isolating $y$ because the resulting equation will have two values of $y$ for some values of $x$ . Hence, this equation does not define $y$ as a function of $x$ .

STEP 11

For the equation $x^{}+y^{}=25$ , we cannot express $y$ as a function of $x$ by isolating $y$ because the resulting equation will have two values of $y$ for some values of $x$ . Hence, this equation does not define $y$ as a function of $x$ .

STEP 12

For the equation $x=y^{2}$ , we cannot express $y$ as a function of $x$ by isolating $y$ because the resulting equation will have two values of $y$ for some values of $x$ . Hence, this equation does not define $y$ as a function of $x$ .

STEP 13

For the equation $x=y^{2}$ , we cannot express $y$ as a function of $x$ by isolating $y$ because the resulting equation will have two values of $y$ for some values of $x$ . Hence, this equation does not define $y$ as a function of $x$ .

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QuestionDetermine if each equation defines y as a function of $x$ : 11. $x+y=16$ , 12. $x+y=25$ , 13. $x^{2}+y=16$ , 14. $x^{2}+y=25$ , 15. $x^{2}+y^{2}=16$ , 16. $x^{2}+y^{2}=25$ , 17. $x=y^{2}$ , 18. $4 x=y^{2}$ .

Studdy Solution

STEP 1

Assumptions1. An equation defines y as a function of x if for every value of x, there is exactly one corresponding value of y. . The equations are given in the form of $x$ and $y$ .

STEP 2

For the equation $x+y=16$ , we can express $y$ as a function of $x$ by isolating $y$ .
$y =16 - x$

STEP 3

In the equation $y =16 - x$ , for each value of $x$ , there is exactly one corresponding value of $y$ . Hence, this equation defines $y$ as a function of $x$ .

STEP 4

For the equation $x+y=25$ , we can express $y$ as a function of $x$ by isolating $y$ .
$y =25 - x$

STEP 5

In the equation $y =25 - x$ , for each value of $x$ , there is exactly one corresponding value of $y$ . Hence, this equation defines $y$ as a function of $x$ .

STEP 6

For the equation $x^{2}+y=16$ , we can express $y$ as a function of $x$ by isolating $y$ .
$y =16 - x^{2}$

STEP 7

In the equation $y =16 - x^{2}$ , for each value of $x$ , there is exactly one corresponding value of $y$ . Hence, this equation defines $y$ as a function of $x$ .

STEP 8

For the equation $x^{2}+y=25$ , we can express $y$ as a function of $x$ by isolating $y$ .
$y =25 - x^{2}$

STEP 9

In the equation $y =25 - x^{2}$ , for each value of $x$ , there is exactly one corresponding value of $y$ . Hence, this equation defines $y$ as a function of $x$ .

STEP 10

For the equation $x^{2}+y^{2}=16$ , we cannot express $y$ as a function of $x$ by isolating $y$ because the resulting equation will have two values of $y$ for some values of $x$ . Hence, this equation does not define $y$ as a function of $x$ .

STEP 11

For the equation $x^{}+y^{}=25$ , we cannot express $y$ as a function of $x$ by isolating $y$ because the resulting equation will have two values of $y$ for some values of $x$ . Hence, this equation does not define $y$ as a function of $x$ .

STEP 12

For the equation $x=y^{2}$ , we cannot express $y$ as a function of $x$ by isolating $y$ because the resulting equation will have two values of $y$ for some values of $x$ . Hence, this equation does not define $y$ as a function of $x$ .

STEP 13

For the equation $x=y^{2}$ , we cannot express $y$ as a function of $x$ by isolating $y$ because the resulting equation will have two values of $y$ for some values of $x$ . Hence, this equation does not define $y$ as a function of $x$ .

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QuestionDetermine if each equation defines y as a function of xxx: 11. x+y=16x+y=16x+y=16, 12. x+y=25x+y=25x+y=25, 13. x2+y=16x^{2}+y=16x2+y=16, 14. x2+y=25x^{2}+y=25x2+y=25, 15. x2+y2=16x^{2}+y^{2}=16x2+y2=16, 16. x2+y2=25x^{2}+y^{2}=25x2+y2=25, 17. x=y2x=y^{2}x=y2, 18. 4x=y24 x=y^{2}4x=y2.

Studdy Solution

STEP 1

Assumptions1. An equation defines y as a function of x if for every value of x, there is exactly one corresponding value of y. . The equations are given in the form of xxx and yyy.

STEP 2

For the equation x+y=16x+y=16x+y=16, we can express yyy as a function of xxx by isolating yyy.y=16−xy =16 - xy=16−x

STEP 3

In the equation y=16−xy =16 - xy=16−x, for each value of xxx, there is exactly one corresponding value of yyy. Hence, this equation defines yyy as a function of xxx.

STEP 4

For the equation x+y=25x+y=25x+y=25, we can express yyy as a function of xxx by isolating yyy.y=25−xy =25 - xy=25−x

STEP 5

In the equation y=25−xy =25 - xy=25−x, for each value of xxx, there is exactly one corresponding value of yyy. Hence, this equation defines yyy as a function of xxx.

STEP 6

For the equation x2+y=16x^{2}+y=16x2+y=16, we can express yyy as a function of xxx by isolating yyy.y=16−x2y =16 - x^{2}y=16−x2

STEP 7

In the equation y=16−x2y =16 - x^{2}y=16−x2, for each value of xxx, there is exactly one corresponding value of yyy. Hence, this equation defines yyy as a function of xxx.

STEP 8

For the equation x2+y=25x^{2}+y=25x2+y=25, we can express yyy as a function of xxx by isolating yyy.y=25−x2y =25 - x^{2}y=25−x2

STEP 9

In the equation y=25−x2y =25 - x^{2}y=25−x2, for each value of xxx, there is exactly one corresponding value of yyy. Hence, this equation defines yyy as a function of xxx.

STEP 10

For the equation x2+y2=16x^{2}+y^{2}=16x2+y2=16, we cannot express yyy as a function of xxx by isolating yyy because the resulting equation will have two values of yyy for some values of xxx. Hence, this equation does not define yyy as a function of xxx.

STEP 11

For the equation x+y=25x^{}+y^{}=25x+y=25, we cannot express yyy as a function of xxx by isolating yyy because the resulting equation will have two values of yyy for some values of xxx. Hence, this equation does not define yyy as a function of xxx.

STEP 12

For the equation x=y2x=y^{2}x=y2, we cannot express yyy as a function of xxx by isolating yyy because the resulting equation will have two values of yyy for some values of xxx. Hence, this equation does not define yyy as a function of xxx.

STEP 13

For the equation x=y2x=y^{2}x=y2, we cannot express yyy as a function of xxx by isolating yyy because the resulting equation will have two values of yyy for some values of xxx. Hence, this equation does not define yyy as a function of xxx.

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QuestionDetermine if each equation defines y as a function of $x$ : 11. $x+y=16$ , 12. $x+y=25$ , 13. $x^{2}+y=16$ , 14. $x^{2}+y=25$ , 15. $x^{2}+y^{2}=16$ , 16. $x^{2}+y^{2}=25$ , 17. $x=y^{2}$ , 18. $4 x=y^{2}$ .

Assumptions1. An equation defines y as a function of x if for every value of x, there is exactly one corresponding value of y. . The equations are given in the form of $x$ and $y$ .

For the equation $x+y=16$ , we can express $y$ as a function of $x$ by isolating $y$ .
$y =16 - x$

In the equation $y =16 - x$ , for each value of $x$ , there is exactly one corresponding value of $y$ . Hence, this equation defines $y$ as a function of $x$ .

For the equation $x+y=25$ , we can express $y$ as a function of $x$ by isolating $y$ .
$y =25 - x$

In the equation $y =25 - x$ , for each value of $x$ , there is exactly one corresponding value of $y$ . Hence, this equation defines $y$ as a function of $x$ .

For the equation $x^{2}+y=16$ , we can express $y$ as a function of $x$ by isolating $y$ .
$y =16 - x^{2}$

In the equation $y =16 - x^{2}$ , for each value of $x$ , there is exactly one corresponding value of $y$ . Hence, this equation defines $y$ as a function of $x$ .

For the equation $x^{2}+y=25$ , we can express $y$ as a function of $x$ by isolating $y$ .
$y =25 - x^{2}$

In the equation $y =25 - x^{2}$ , for each value of $x$ , there is exactly one corresponding value of $y$ . Hence, this equation defines $y$ as a function of $x$ .

For the equation $x^{2}+y^{2}=16$ , we cannot express $y$ as a function of $x$ by isolating $y$ because the resulting equation will have two values of $y$ for some values of $x$ . Hence, this equation does not define $y$ as a function of $x$ .

For the equation $x^{}+y^{}=25$ , we cannot express $y$ as a function of $x$ by isolating $y$ because the resulting equation will have two values of $y$ for some values of $x$ . Hence, this equation does not define $y$ as a function of $x$ .

For the equation $x=y^{2}$ , we cannot express $y$ as a function of $x$ by isolating $y$ because the resulting equation will have two values of $y$ for some values of $x$ . Hence, this equation does not define $y$ as a function of $x$ .

For the equation $x=y^{2}$ , we cannot express $y$ as a function of $x$ by isolating $y$ because the resulting equation will have two values of $y$ for some values of $x$ . Hence, this equation does not define $y$ as a function of $x$ .