QuestionIdentify the linear function from these equations: $f(x)=\frac{3 x+2}{4}$ , $f(x)=\sqrt{x+2}$ , $f(x)=2 x^{2 x-3}$ , $f(x)=\frac{3 x-3}{x^{2}}$ .

Studdy Solution

STEP 1

Assumptions1. A linear function is a function of the form $f(x) = mx + c$ , where $m$ and $c$ are constants. . $m$ is the slope of the line and $c$ is the y-intercept.
3. A linear function graph is a straight line.

STEP 2

We need to identify which of the given functions is of the form $f(x) = mx + c$ .

STEP 3

Let's start with the first function $f(x)=\frac{3x+2}{}$ .

STEP 4

We can rewrite this function as $f(x) = \frac{3}{4}x + \frac{2}{4}$ .

STEP 5

This function is of the form $f(x) = mx + c$ , where $m = \frac{3}{4}$ and $c = \frac{2}{4}$ . So, this is a linear function.

STEP 6

Now, let's move to the second function $f(x)=\sqrt{x+2}$ .

STEP 7

This function is not of the form $f(x) = mx + c$ . It involves a square root operation, so it is not a linear function.

STEP 8

Let's consider the third function $f(x)=2x^{2x-3}$ .

STEP 9

This function is not of the form $f(x) = mx + c$ . It involves an exponent that is a function of $x$ , so it is not a linear function.

STEP 10

Finally, let's consider the fourth function $f(x)=\frac{3x-3}{x^{2}}$ .

STEP 11

This function is not of the form $f(x) = mx + c$ . The $x$ term is in the denominator and squared, so it is not a linear function.

STEP 12

After analyzing all the functions, we can conclude that the first function $f(x)=\frac{x+2}{4}$ is the linear function.
The linear function is $f(x)=\frac{x+2}{4}$ .

Was this helpful?

QuestionIdentify the linear function from these equations: $f(x)=\frac{3 x+2}{4}$ , $f(x)=\sqrt{x+2}$ , $f(x)=2 x^{2 x-3}$ , $f(x)=\frac{3 x-3}{x^{2}}$ .

Studdy Solution

STEP 1

Assumptions1. A linear function is a function of the form $f(x) = mx + c$ , where $m$ and $c$ are constants. . $m$ is the slope of the line and $c$ is the y-intercept.
3. A linear function graph is a straight line.

STEP 2

We need to identify which of the given functions is of the form $f(x) = mx + c$ .

STEP 3

Let's start with the first function $f(x)=\frac{3x+2}{}$ .

STEP 4

We can rewrite this function as $f(x) = \frac{3}{4}x + \frac{2}{4}$ .

STEP 5

This function is of the form $f(x) = mx + c$ , where $m = \frac{3}{4}$ and $c = \frac{2}{4}$ . So, this is a linear function.

STEP 6

Now, let's move to the second function $f(x)=\sqrt{x+2}$ .

STEP 7

This function is not of the form $f(x) = mx + c$ . It involves a square root operation, so it is not a linear function.

STEP 8

Let's consider the third function $f(x)=2x^{2x-3}$ .

STEP 9

This function is not of the form $f(x) = mx + c$ . It involves an exponent that is a function of $x$ , so it is not a linear function.

STEP 10

Finally, let's consider the fourth function $f(x)=\frac{3x-3}{x^{2}}$ .

STEP 11

This function is not of the form $f(x) = mx + c$ . The $x$ term is in the denominator and squared, so it is not a linear function.

STEP 12

After analyzing all the functions, we can conclude that the first function $f(x)=\frac{x+2}{4}$ is the linear function.
The linear function is $f(x)=\frac{x+2}{4}$ .

Get Studdy

Studdy solves anything!

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

QuestionIdentify the linear function from these equations: f(x)=3x+24f(x)=\frac{3 x+2}{4}f(x)=43x+2​, f(x)=x+2f(x)=\sqrt{x+2}f(x)=x+2​, f(x)=2x2x−3f(x)=2 x^{2 x-3}f(x)=2x2x−3, f(x)=3x−3x2f(x)=\frac{3 x-3}{x^{2}}f(x)=x23x−3​.

Studdy Solution

STEP 1

Assumptions1. A linear function is a function of the form f(x)=mx+cf(x) = mx + cf(x)=mx+c, where mmm and ccc are constants. . mmm is the slope of the line and ccc is the y-intercept.3. A linear function graph is a straight line.

STEP 2

We need to identify which of the given functions is of the form f(x)=mx+cf(x) = mx + cf(x)=mx+c.

STEP 3

Let's start with the first function f(x)=3x+2f(x)=\frac{3x+2}{}f(x)=3x+2​.

STEP 4

We can rewrite this function as f(x)=34x+24f(x) = \frac{3}{4}x + \frac{2}{4}f(x)=43​x+42​.

STEP 5

This function is of the form f(x)=mx+cf(x) = mx + cf(x)=mx+c, where m=34m = \frac{3}{4}m=43​ and c=24c = \frac{2}{4}c=42​. So, this is a linear function.

STEP 6

Now, let's move to the second function f(x)=x+2f(x)=\sqrt{x+2}f(x)=x+2​.

STEP 7

This function is not of the form f(x)=mx+cf(x) = mx + cf(x)=mx+c. It involves a square root operation, so it is not a linear function.

STEP 8

Let's consider the third function f(x)=2x2x−3f(x)=2x^{2x-3}f(x)=2x2x−3.

STEP 9

This function is not of the form f(x)=mx+cf(x) = mx + cf(x)=mx+c. It involves an exponent that is a function of xxx, so it is not a linear function.

STEP 10

Finally, let's consider the fourth function f(x)=3x−3x2f(x)=\frac{3x-3}{x^{2}}f(x)=x23x−3​.

STEP 11

This function is not of the form f(x)=mx+cf(x) = mx + cf(x)=mx+c. The xxx term is in the denominator and squared, so it is not a linear function.

STEP 12

After analyzing all the functions, we can conclude that the first function f(x)=x+24f(x)=\frac{x+2}{4}f(x)=4x+2​ is the linear function.The linear function is f(x)=x+24f(x)=\frac{x+2}{4}f(x)=4x+2​.

Get Studdy

Studdy solves anything!

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

QuestionIdentify the linear function from these equations: $f(x)=\frac{3 x+2}{4}$ , $f(x)=\sqrt{x+2}$ , $f(x)=2 x^{2 x-3}$ , $f(x)=\frac{3 x-3}{x^{2}}$ .

Assumptions1. A linear function is a function of the form $f(x) = mx + c$ , where $m$ and $c$ are constants. . $m$ is the slope of the line and $c$ is the y-intercept.
3. A linear function graph is a straight line.

We need to identify which of the given functions is of the form $f(x) = mx + c$ .

Let's start with the first function $f(x)=\frac{3x+2}{}$ .

We can rewrite this function as $f(x) = \frac{3}{4}x + \frac{2}{4}$ .

This function is of the form $f(x) = mx + c$ , where $m = \frac{3}{4}$ and $c = \frac{2}{4}$ . So, this is a linear function.

Now, let's move to the second function $f(x)=\sqrt{x+2}$ .

This function is not of the form $f(x) = mx + c$ . It involves a square root operation, so it is not a linear function.

Let's consider the third function $f(x)=2x^{2x-3}$ .

This function is not of the form $f(x) = mx + c$ . It involves an exponent that is a function of $x$ , so it is not a linear function.

Finally, let's consider the fourth function $f(x)=\frac{3x-3}{x^{2}}$ .

This function is not of the form $f(x) = mx + c$ . The $x$ term is in the denominator and squared, so it is not a linear function.

After analyzing all the functions, we can conclude that the first function $f(x)=\frac{x+2}{4}$ is the linear function.
The linear function is $f(x)=\frac{x+2}{4}$ .