Math Snap

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 $x$.

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 $x$.