**Rewrite the Following Equation as a Function of x: A Step-by-Step Guide**

Are you struggling to rewrite equations into functions of specific variables? Don’t worry, you’re not alone. Many students and professionals face challenges in understanding this fundamental mathematical concept. In this blog post, we’ll simplify the process by providing a step-by-step guide to rewrite the following equation as a function of x.

**The Need for Equation Manipulation**

In various fields like engineering, science, and finance, we often encounter equations that need to be manipulated and rewritten to fit specific requirements. This can include rewriting an equation as a function of a particular variable, like x. By doing so, we gain a deeper understanding of the equation’s behavior and can apply it effectively in problem-solving.

**Steps to Rewrite the Equation**

To rewrite an equation as a function of x, follow these steps:

**Isolate the variable (x):**Manipulate the equation using algebraic operations to move the x-term alone to one side of the equals sign.**Simplify the other side:**Perform necessary calculations on the remaining terms to obtain a single expression.**Express as an equation:**Introduce the variable y (or any other variable) to represent the value of the simplified side. This gives you the equation y = [simplified side].

**Summary**

Rewriting an equation as a function of x involves isolating the variable, simplifying the other terms, and expressing it as a new equation. By following the steps outlined above, you can confidently transform equations into functions of specific variables, unlocking their potential for further analysis and problem-solving.

## Rewrite the Equation as a Function of x

### Introduction

The given equation represents a relationship between variables. To rewrite it as a function of x, we need to isolate x on one side of the equation and express y in terms of x.

### Steps to Rewrite the Equation

**Start with the Given Equation:**

```
y = 2x - 5
```

**Subtract 5 from Both Sides:**

```
y - 5 = 2x - 5 - 5
```

```
y - 5 = 2x - 10
```

**Factor Out 2 from the Right Side:**

```
y - 5 = 2(x - 5)
```

**Divide Both Sides by 2:**

```
(y - 5) / 2 = x - 5
```

**Simplify the Left Side:**

```
(y - 5) / 2 = x - 5
```

```
1/2y - 5/2 = x - 5
```

**Add 5/2 to Both Sides:**

```
1/2y - 5/2 + 5/2 = x - 5 + 5/2
```

```
1/2y = x - 5/2
```

**Multiply Both Sides by 2 to Isolate y:**

```
2 * 1/2y = 2 * (x - 5/2)
```

```
y = 2x - 5
```

### Function of x

Therefore, the equation rewritten as a function of x is:

```
f(x) = 2x - 5
```

### Image: Graph of the Function

[Image of the graph of the function f(x) = 2x – 5]

https://tse1.mm.bing.net/th?q=graph+of+the+function+f(x)+%3D+2x+-+5

### Additional Notes

- The original equation is linear and represents a straight line.
- The function f(x) has a slope of 2 and a y-intercept of -5.
- The function is increasing (positively sloped).

### Conclusion

We have successfully rewritten the given equation as a function of x: f(x) = 2x – 5. This form allows us to determine the corresponding y-value for any given value of x.

### Frequently Asked Questions (FAQs)

**What is the domain of the function f(x)?**

- All real numbers.

**What is the range of the function f(x)?**

- All real numbers.

**What is the x-intercept of the function f(x)?**

- 2.5

**What is the y-intercept of the function f(x)?**

- -5

**Is the function f(x) even or odd?**

- Neither (it is an odd function).

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