Find The Zero Of The Linear Function: $f(x) = 2 + 5x$A. $\frac{2}{5}$

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Introduction

In mathematics, a linear function is a polynomial function of degree one, which means it has the form f(x)=ax+bf(x) = ax + b, where aa and bb are constants. The zero of a linear function is the value of xx that makes the function equal to zero. In other words, it is the solution to the equation f(x)=0f(x) = 0. In this article, we will focus on finding the zero of the linear function f(x)=2+5xf(x) = 2 + 5x.

What is a Linear Function?

A linear function is a function that can be written in the form f(x)=ax+bf(x) = ax + b, where aa and bb are constants. The graph of a linear function is a straight line, and the function can be represented by a linear equation. Linear functions are used to model a wide range of real-world phenomena, including population growth, cost functions, and supply and demand curves.

The Zero of a Linear Function

The zero of a linear function is the value of xx that makes the function equal to zero. In other words, it is the solution to the equation f(x)=0f(x) = 0. To find the zero of a linear function, we can set the function equal to zero and solve for xx. This can be done using algebraic methods, such as factoring or the quadratic formula.

Finding the Zero of the Linear Function f(x)=2+5xf(x) = 2 + 5x

To find the zero of the linear function f(x)=2+5xf(x) = 2 + 5x, we can set the function equal to zero and solve for xx. This gives us the equation:

2+5x=02 + 5x = 0

We can solve this equation by subtracting 2 from both sides, which gives us:

5x=−25x = -2

Next, we can divide both sides by 5, which gives us:

x=−25x = -\frac{2}{5}

Therefore, the zero of the linear function f(x)=2+5xf(x) = 2 + 5x is x=−25x = -\frac{2}{5}.

Why is Finding the Zero of a Linear Function Important?

Finding the zero of a linear function is an important concept in mathematics and has many practical applications. For example, in economics, the zero of a linear function can represent the break-even point of a business, where the revenue equals the cost. In physics, the zero of a linear function can represent the equilibrium point of a system, where the net force acting on the system is zero.

Conclusion

In conclusion, finding the zero of a linear function is an important concept in mathematics that has many practical applications. By understanding how to find the zero of a linear function, we can solve a wide range of problems in mathematics and other fields. In this article, we have focused on finding the zero of the linear function f(x)=2+5xf(x) = 2 + 5x, and we have shown that the zero of this function is x=−25x = -\frac{2}{5}.

Frequently Asked Questions

Q: What is a linear function?

A: A linear function is a polynomial function of degree one, which means it has the form f(x)=ax+bf(x) = ax + b, where aa and bb are constants.

Q: What is the zero of a linear function?

A: The zero of a linear function is the value of xx that makes the function equal to zero. In other words, it is the solution to the equation f(x)=0f(x) = 0.

Q: How do I find the zero of a linear function?

A: To find the zero of a linear function, you can set the function equal to zero and solve for xx using algebraic methods, such as factoring or the quadratic formula.

Q: Why is finding the zero of a linear function important?

A: Finding the zero of a linear function is important because it has many practical applications in mathematics and other fields, such as economics and physics.

References

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Q: What is a linear function?

A: A linear function is a polynomial function of degree one, which means it has the form f(x)=ax+bf(x) = ax + b, where aa and bb are constants.

Q: What is the zero of a linear function?

A: The zero of a linear function is the value of xx that makes the function equal to zero. In other words, it is the solution to the equation f(x)=0f(x) = 0.

Q: How do I find the zero of a linear function?

A: To find the zero of a linear function, you can set the function equal to zero and solve for xx using algebraic methods, such as factoring or the quadratic formula.

Q: What is the difference between a linear function and a quadratic function?

A: A linear function is a polynomial function of degree one, while a quadratic function is a polynomial function of degree two. A linear function has the form f(x)=ax+bf(x) = ax + b, while a quadratic function has the form f(x)=ax2+bx+cf(x) = ax^2 + bx + c.

Q: Can a linear function have more than one zero?

A: No, a linear function can only have one zero. This is because a linear function is a straight line, and a straight line can only intersect the x-axis at one point.

Q: How do I know if a linear function has a zero?

A: To determine if a linear function has a zero, you can set the function equal to zero and solve for xx. If the equation has a solution, then the linear function has a zero.

Q: What is the significance of the zero of a linear function?

A: The zero of a linear function is significant because it represents the point where the function intersects the x-axis. This point is also known as the x-intercept.

Q: Can a linear function have a zero at the origin?

A: Yes, a linear function can have a zero at the origin. This means that the function intersects the x-axis at the point (0,0).

Q: How do I find the zero of a linear function with a negative slope?

A: To find the zero of a linear function with a negative slope, you can set the function equal to zero and solve for xx. Since the slope is negative, the function will intersect the x-axis at a point to the left of the origin.

Q: Can a linear function have a zero at a point other than the origin?

A: Yes, a linear function can have a zero at a point other than the origin. This means that the function intersects the x-axis at a point other than (0,0).

Q: How do I find the zero of a linear function with a positive slope?

A: To find the zero of a linear function with a positive slope, you can set the function equal to zero and solve for xx. Since the slope is positive, the function will intersect the x-axis at a point to the right of the origin.

Q: What is the relationship between the zero of a linear function and its slope?

A: The zero of a linear function is related to its slope. If the slope is positive, the function will intersect the x-axis at a point to the right of the origin. If the slope is negative, the function will intersect the x-axis at a point to the left of the origin.

Q: Can a linear function have a zero at a point that is not an integer?

A: Yes, a linear function can have a zero at a point that is not an integer. This means that the function intersects the x-axis at a point that is a decimal or a fraction.

Q: How do I find the zero of a linear function with a fractional slope?

A: To find the zero of a linear function with a fractional slope, you can set the function equal to zero and solve for xx. Since the slope is fractional, the function will intersect the x-axis at a point that is a decimal or a fraction.

Q: Can a linear function have a zero at a point that is a negative number?

A: Yes, a linear function can have a zero at a point that is a negative number. This means that the function intersects the x-axis at a point that is to the left of the origin.

Q: How do I find the zero of a linear function with a negative slope and a fractional coefficient?

A: To find the zero of a linear function with a negative slope and a fractional coefficient, you can set the function equal to zero and solve for xx. Since the slope is negative and the coefficient is fractional, the function will intersect the x-axis at a point that is a decimal or a fraction to the left of the origin.

Q: Can a linear function have a zero at a point that is a complex number?

A: No, a linear function cannot have a zero at a point that is a complex number. This is because a linear function is a real-valued function, and complex numbers are not real numbers.

Q: How do I find the zero of a linear function with a complex coefficient?

A: To find the zero of a linear function with a complex coefficient, you can set the function equal to zero and solve for xx. Since the coefficient is complex, the function will not intersect the x-axis at a real point.

Q: Can a linear function have a zero at a point that is a vector?

A: No, a linear function cannot have a zero at a point that is a vector. This is because a linear function is a real-valued function, and vectors are not real numbers.

Q: How do I find the zero of a linear function with a vector coefficient?

A: To find the zero of a linear function with a vector coefficient, you can set the function equal to zero and solve for xx. Since the coefficient is a vector, the function will not intersect the x-axis at a real point.

Q: Can a linear function have a zero at a point that is a matrix?

A: No, a linear function cannot have a zero at a point that is a matrix. This is because a linear function is a real-valued function, and matrices are not real numbers.

Q: How do I find the zero of a linear function with a matrix coefficient?

A: To find the zero of a linear function with a matrix coefficient, you can set the function equal to zero and solve for xx. Since the coefficient is a matrix, the function will not intersect the x-axis at a real point.

Q: Can a linear function have a zero at a point that is a function?

A: No, a linear function cannot have a zero at a point that is a function. This is because a linear function is a real-valued function, and functions are not real numbers.

Q: How do I find the zero of a linear function with a function coefficient?

A: To find the zero of a linear function with a function coefficient, you can set the function equal to zero and solve for xx. Since the coefficient is a function, the function will not intersect the x-axis at a real point.

Q: Can a linear function have a zero at a point that is a set?

A: No, a linear function cannot have a zero at a point that is a set. This is because a linear function is a real-valued function, and sets are not real numbers.

Q: How do I find the zero of a linear function with a set coefficient?

A: To find the zero of a linear function with a set coefficient, you can set the function equal to zero and solve for xx. Since the coefficient is a set, the function will not intersect the x-axis at a real point.

Q: Can a linear function have a zero at a point that is a relation?

A: No, a linear function cannot have a zero at a point that is a relation. This is because a linear function is a real-valued function, and relations are not real numbers.

Q: How do I find the zero of a linear function with a relation coefficient?

A: To find the zero of a linear function with a relation coefficient, you can set the function equal to zero and solve for xx. Since the coefficient is a relation, the function will not intersect the x-axis at a real point.

Q: Can a linear function have a zero at a point that is a number?

A: Yes, a linear function can have a zero at a point that is a number. This means that the function intersects the x-axis at a point that is a real number.

Q: How do I find the zero of a linear function with a number coefficient?

A: To find the zero of a linear function with a number coefficient, you can set the function equal to zero and solve for xx. Since the coefficient is a number, the function will intersect the x-axis at a real point.

Q: Can a linear function have a zero at a point that is a real number?

A: Yes, a linear function can have a zero at a point that is a real number. This means that the function intersects the x-axis at a point that is a real number.

Q: How do I find the zero of a linear function with a real number coefficient?

A: To find the zero of a linear function with a real number coefficient, you can set the function equal to zero and solve for xx. Since the coefficient