What Is The { Y $}$-intercept Of The Function { F(x) = 4 - 5x $}$?A. { -5$}$B. { -4$}$C. 4D. 5

$$$$

Understanding the $y$-intercept

The $y$-intercept of a function is the point at which the graph of the function intersects the $y$-axis. In other words, it is the value of $y$ when $x$ is equal to zero. To find the $y$-intercept of a function, we need to substitute $x = 0$ into the equation of the function and solve for $y$.

Finding the $y$-intercept of the function $f(x) = 4 - 5x$

To find the $y$-intercept of the function $f(x) = 4 - 5x$, we need to substitute $x = 0$ into the equation of the function. This gives us:

$f(0) = 4 - 5(0)$

Simplifying the equation, we get:

$f(0) = 4 - 0$

$f(0) = 4$

Therefore, the $y$-intercept of the function $f(x) = 4 - 5x$ is 4.

Why is the $y$-intercept important?

The $y$-intercept is an important concept in mathematics, particularly in algebra and calculus. It is used to determine the behavior of a function at a specific point, and it can be used to find the equation of a line or a curve. In addition, the $y$-intercept is used in various real-world applications, such as physics, engineering, and economics.

How to find the $y$-intercept of a function

To find the $y$-intercept of a function, we need to follow these steps:

1. Substitute $x = 0$ into the equation of the function.
2. Simplify the equation to find the value of $y$.
3. The value of $y$ is the $y$-intercept of the function.

Examples of finding the $y$-intercept

Here are some examples of finding the $y$-intercept of a function:

• Find the $y$-intercept of the function $f(x) = 2x + 3$.
• Find the $y$-intercept of the function $f(x) = x^2 - 4$.
• Find the $y$-intercept of the function $f(x) = 3x - 2$.

Conclusion

In conclusion, the $y$-intercept of a function is the point at which the graph of the function intersects the $y$-axis. To find the $y$-intercept of a function, we need to substitute $x = 0$ into the equation of the function and solve for $y$. The $y$-intercept is an important concept in mathematics, and it is used in various real-world applications.

Frequently Asked Questions

• What is the $y$-intercept of a function?
• How to find the $y$-intercept of a function?
• Why is the $y$-intercept important?

Final Answer

The final answer is: $\boxed{4}$

$$

Q: What is the $y$-intercept of a function?

A: The $y$-intercept of a function is the point at which the graph of the function intersects the $y$-axis. It is the value of $y$ when $x$ is equal to zero.

Q: How to find the $y$-intercept of a function?

A: To find the $y$-intercept of a function, we need to substitute $x = 0$ into the equation of the function and solve for $y$. This can be done by following these steps:

1. Substitute $x = 0$ into the equation of the function.
2. Simplify the equation to find the value of $y$.
3. The value of $y$ is the $y$-intercept of the function.

Q: Why is the $y$-intercept important?

A: The $y$-intercept is an important concept in mathematics, particularly in algebra and calculus. It is used to determine the behavior of a function at a specific point, and it can be used to find the equation of a line or a curve. In addition, the $y$-intercept is used in various real-world applications, such as physics, engineering, and economics.

Q: What is the difference between the $y$-intercept and the $x$-intercept?

A: The $y$-intercept is the point at which the graph of a function intersects the $y$-axis, while the $x$-intercept is the point at which the graph of a function intersects the $x$-axis. In other words, the $y$-intercept is the value of $y$ when $x$ is equal to zero, while the $x$-intercept is the value of $x$ when $y$ is equal to zero.

Q: Can a function have more than one $y$-intercept?

A: No, a function can only have one $y$-intercept. The $y$-intercept is a unique point on the graph of a function, and it is determined by the equation of the function.

Q: How to find the $y$-intercept of a quadratic function?

A: To find the $y$-intercept of a quadratic function, we need to substitute $x = 0$ into the equation of the function and solve for $y$. This can be done by following these steps:

1. Substitute $x = 0$ into the equation of the function.
2. Simplify the equation to find the value of $y$.
3. The value of $y$ is the $y$-intercept of the function.

Q: Can the $y$-intercept be a complex number?

A: Yes, the $y$-intercept can be a complex number. If the equation of the function has complex roots, then the $y$-intercept will be a complex number.

Q: How to find the $y$-intercept of a function with a negative exponent?

A: To find the $y$-intercept of a function with a negative exponent, we need to substitute $x = 0$ into the equation of the function and solve for $y$. This can be done by following these steps:

1. Substitute $x = 0$ into the equation of the function.
2. Simplify the equation to find the value of $y$.
3. The value of $y$ is the $y$-intercept of the function.

Q: Can the $y$-intercept be a fraction?

A: Yes, the $y$-intercept can be a fraction. If the equation of the function has a fraction as a coefficient, then the $y$-intercept will be a fraction.

Q: How to find the $y$-intercept of a function with a variable in the exponent?

A: To find the $y$-intercept of a function with a variable in the exponent, we need to substitute $x = 0$ into the equation of the function and solve for $y$. This can be done by following these steps:

1. Substitute $x = 0$ into the equation of the function.
2. Simplify the equation to find the value of $y$.
3. The value of $y$ is the $y$-intercept of the function.

Q: Can the $y$-intercept be a negative number?

A: Yes, the $y$-intercept can be a negative number. If the equation of the function has a negative coefficient, then the $y$-intercept will be a negative number.

Q: How to find the $y$-intercept of a function with a logarithmic term?

A: To find the $y$-intercept of a function with a logarithmic term, we need to substitute $x = 0$ into the equation of the function and solve for $y$. This can be done by following these steps:

1. Substitute $x = 0$ into the equation of the function.
2. Simplify the equation to find the value of $y$.
3. The value of $y$ is the $y$-intercept of the function.

Q: Can the $y$-intercept be a transcendental number?

A: Yes, the $y$-intercept can be a transcendental number. If the equation of the function has a transcendental term, then the $y$-intercept will be a transcendental number.

Q: How to find the $y$-intercept of a function with a trigonometric term?

A: To find the $y$-intercept of a function with a trigonometric term, we need to substitute $x = 0$ into the equation of the function and solve for $y$. This can be done by following these steps:

1. Substitute $x = 0$ into the equation of the function.
2. Simplify the equation to find the value of $y$.
3. The value of $y$ is the $y$-intercept of the function.

Q: Can the $y$-intercept be a periodic function?

A: Yes, the $y$-intercept can be a periodic function. If the equation of the function has a periodic term, then the $y$-intercept will be a periodic function.

Q: How to find the $y$-intercept of a function with a rational term?

A: To find the $y$-intercept of a function with a rational term, we need to substitute $x = 0$ into the equation of the function and solve for $y$. This can be done by following these steps:

1. Substitute $x = 0$ into the equation of the function.
2. Simplify the equation to find the value of $y$.
3. The value of $y$ is the $y$-intercept of the function.

Q: Can the $y$-intercept be a function of a function?

A: Yes, the $y$-intercept can be a function of a function. If the equation of the function has a function as a coefficient, then the $y$-intercept will be a function of a function.

Q: How to find the $y$-intercept of a function with a function as a coefficient?

A: To find the $y$-intercept of a function with a function as a coefficient, we need to substitute $x = 0$ into the equation of the function and solve for $y$. This can be done by following these steps:

1. Substitute $x = 0$ into the equation of the function.
2. Simplify the equation to find the value of $y$.
3. The value of $y$ is the $y$-intercept of the function.

Q: Can the $y$-intercept be a function of a variable?

A: Yes, the $y$-intercept can be a function of a variable. If the equation of the function has a variable as a coefficient, then the $y$-intercept will be a function of a variable.

Q: How to find the $y$-intercept of a function with a variable as a coefficient?

A: To find the $y$-intercept of a function with a variable as a coefficient, we need to substitute $x = 0$ into the equation of the function and solve for $y$. This can be done by following these steps:

1. Substitute $x = 0$ into the equation of the function.
2. Simplify the equation to find the value of $y$.
3. The value of $y$ is the $y$-intercept of the function.

Q: Can the $y$-intercept be a function of a constant?

A: Yes, the $y$-intercept can be a function of a constant. If the equation of the function has a constant as a coefficient, then the $y$-intercept will be a function of a constant.

Q: How to find the $y$-intercept of a function with a constant as a coefficient?

A: To find the $y$-intercept of a function with a constant as a coefficient, we need to substitute $x = 0$ into the equation of the function and solve for $y$. This can be done by following these steps:

1. Substitute $x = 0$ into the equation of the function.
2. Simplify