Solved on Oct 27, 2023

Identify the reciprocal functions from the given equations: $y=x^{2}$ , $y=\frac{1}{x+4}$ , $y=\frac{7}{x}$ , $y=\frac{2}{x}+5$ , $y=\frac{x}{8}$ , $y=3 x+1$ .

STEP 1

Assumptions1. A reciprocal function is a function of the form $y = \frac{a}{x} + b$ , where $a$ and $b$ are constants, and $x$ is the variable. . The functions provided are in the correct form and are simplified.

STEP 2

We need to identify which of the given equations are in the form of a reciprocal function. We can do this by comparing each equation with the standard form of a reciprocal function.

STEP 3

The first equation is $y = x^{2}$ . This is not in the form of a reciprocal function because the variable $x$ is not in the denominator.

STEP 4

The second equation is $y = \frac{1}{x+4}$ . This is not in the form of a reciprocal function because there is a constant added to the variable $x$ in the denominator.

STEP 5

The third equation is $y = \frac{7}{x}$ . This is in the form of a reciprocal function because the variable $x$ is in the denominator and there is a constant in the numerator.

STEP 6

The fourth equation is $y = \frac{2}{x} +5$ . This is in the form of a reciprocal function because the variable $x$ is in the denominator and there is a constant in the numerator. The constant added to the fraction does not change the fact that this is a reciprocal function.

STEP 7

The fifth equation is $y = \frac{x}{}$ . This is not in the form of a reciprocal function because the variable $x$ is in the numerator.

STEP 8

The sixth equation is $y =3x +1$ . This is not in the form of a reciprocal function because the variable $x$ is not in the denominator.
The equations that are reciprocal functions are $y = \frac{7}{x}$ and $y = \frac{2}{x} +5$ .

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Identify the reciprocal functions from the given equations: $y=x^{2}$ , $y=\frac{1}{x+4}$ , $y=\frac{7}{x}$ , $y=\frac{2}{x}+5$ , $y=\frac{x}{8}$ , $y=3 x+1$ .

STEP 1

Assumptions1. A reciprocal function is a function of the form $y = \frac{a}{x} + b$ , where $a$ and $b$ are constants, and $x$ is the variable. . The functions provided are in the correct form and are simplified.

STEP 2

We need to identify which of the given equations are in the form of a reciprocal function. We can do this by comparing each equation with the standard form of a reciprocal function.

STEP 3

The first equation is $y = x^{2}$ . This is not in the form of a reciprocal function because the variable $x$ is not in the denominator.

STEP 4

The second equation is $y = \frac{1}{x+4}$ . This is not in the form of a reciprocal function because there is a constant added to the variable $x$ in the denominator.

STEP 5

The third equation is $y = \frac{7}{x}$ . This is in the form of a reciprocal function because the variable $x$ is in the denominator and there is a constant in the numerator.

STEP 6

The fourth equation is $y = \frac{2}{x} +5$ . This is in the form of a reciprocal function because the variable $x$ is in the denominator and there is a constant in the numerator. The constant added to the fraction does not change the fact that this is a reciprocal function.

STEP 7

The fifth equation is $y = \frac{x}{}$ . This is not in the form of a reciprocal function because the variable $x$ is in the numerator.

STEP 8

The sixth equation is $y =3x +1$ . This is not in the form of a reciprocal function because the variable $x$ is not in the denominator.
The equations that are reciprocal functions are $y = \frac{7}{x}$ and $y = \frac{2}{x} +5$ .

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Identify the reciprocal functions from the given equations: y=x2y=x^{2}y=x2, y=1x+4y=\frac{1}{x+4}y=x+41​, y=7xy=\frac{7}{x}y=x7​, y=2x+5y=\frac{2}{x}+5y=x2​+5, y=x8y=\frac{x}{8}y=8x​, y=3x+1y=3 x+1y=3x+1.

STEP 1

Assumptions1. A reciprocal function is a function of the form y=ax+by = \frac{a}{x} + by=xa​+b, where aaa and bbb are constants, and xxx is the variable. . The functions provided are in the correct form and are simplified.

STEP 2

We need to identify which of the given equations are in the form of a reciprocal function. We can do this by comparing each equation with the standard form of a reciprocal function.

STEP 3

The first equation is y=x2y = x^{2}y=x2. This is not in the form of a reciprocal function because the variable xxx is not in the denominator.

STEP 4

The second equation is y=1x+4y = \frac{1}{x+4}y=x+41​. This is not in the form of a reciprocal function because there is a constant added to the variable xxx in the denominator.

STEP 5

The third equation is y=7xy = \frac{7}{x}y=x7​. This is in the form of a reciprocal function because the variable xxx is in the denominator and there is a constant in the numerator.

STEP 6

The fourth equation is y=2x+5y = \frac{2}{x} +5y=x2​+5. This is in the form of a reciprocal function because the variable xxx is in the denominator and there is a constant in the numerator. The constant added to the fraction does not change the fact that this is a reciprocal function.

STEP 7

The fifth equation is y=xy = \frac{x}{}y=x​. This is not in the form of a reciprocal function because the variable xxx is in the numerator.

STEP 8

The sixth equation is y=3x+1y =3x +1y=3x+1. This is not in the form of a reciprocal function because the variable xxx is not in the denominator.The equations that are reciprocal functions are y=7xy = \frac{7}{x}y=x7​ and y=2x+5y = \frac{2}{x} +5y=x2​+5.

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Identify the reciprocal functions from the given equations: $y=x^{2}$ , $y=\frac{1}{x+4}$ , $y=\frac{7}{x}$ , $y=\frac{2}{x}+5$ , $y=\frac{x}{8}$ , $y=3 x+1$ .

Assumptions1. A reciprocal function is a function of the form $y = \frac{a}{x} + b$ , where $a$ and $b$ are constants, and $x$ is the variable. . The functions provided are in the correct form and are simplified.

The first equation is $y = x^{2}$ . This is not in the form of a reciprocal function because the variable $x$ is not in the denominator.

The second equation is $y = \frac{1}{x+4}$ . This is not in the form of a reciprocal function because there is a constant added to the variable $x$ in the denominator.

The third equation is $y = \frac{7}{x}$ . This is in the form of a reciprocal function because the variable $x$ is in the denominator and there is a constant in the numerator.

The fourth equation is $y = \frac{2}{x} +5$ . This is in the form of a reciprocal function because the variable $x$ is in the denominator and there is a constant in the numerator. The constant added to the fraction does not change the fact that this is a reciprocal function.

The fifth equation is $y = \frac{x}{}$ . This is not in the form of a reciprocal function because the variable $x$ is in the numerator.

The sixth equation is $y =3x +1$ . This is not in the form of a reciprocal function because the variable $x$ is not in the denominator.
The equations that are reciprocal functions are $y = \frac{7}{x}$ and $y = \frac{2}{x} +5$ .