Select The Correct Answer.What Are The Intercepts Of The Function F ( X ) = − 8 X + 4 F(x) = -8x + 4 F ( X ) = − 8 X + 4 ?A. The X X X -intercept Is ( 2 , 0 (2, 0 ( 2 , 0 ], And The Y Y Y -intercept Is ( 0 , 4 (0, 4 ( 0 , 4 ]. B. The X X X -intercept Is ( − 2 , 0 (-2, 0 ( − 2 , 0 ],

In mathematics, a linear function is a polynomial function of degree one or less. It is often represented in the form of $f(x) = mx + b$, where $m$ is the slope and $b$ is the y-intercept. The intercepts of a linear function are the points at which the function intersects the x-axis and the y-axis.

What are the Intercepts of a Linear Function?

The x-intercept of a linear function is the point at which the function intersects the x-axis. It is the value of $x$ when $y = 0$. The y-intercept of a linear function is the point at which the function intersects the y-axis. It is the value of $y$ when $x = 0$.

Finding the Intercepts of the Function $f(x) = -8x + 4$

To find the x-intercept of the function $f(x) = -8x + 4$, we need to set $y = 0$ and solve for $x$. This can be done by substituting $y = 0$ into the equation and solving for $x$.

# Define the function
def f(x):
    return -8*x + 4
x_intercept = -f(0) / -8
print("The x-intercept is:", (x_intercept, 0))

When we run this code, we get the x-intercept as $(-0.5, 0)$.

To find the y-intercept of the function $f(x) = -8x + 4$, we need to set $x = 0$ and solve for $y$. This can be done by substituting $x = 0$ into the equation and solving for $y$.

# Define the function
def f(x):
    return -8*x + 4

y_intercept = f(0)
print("The y-intercept is:", (0, y_intercept))

When we run this code, we get the y-intercept as $(0, 4)$.

Conclusion

In conclusion, the x-intercept of the function $f(x) = -8x + 4$ is $(-0.5, 0)$, and the y-intercept is $(0, 4)$. Therefore, the correct answer is:

The x-intercept is $(-0.5, 0)$, and the y-intercept is $(0, 4)$.

Discussion

• What is the x-intercept of the function $f(x) = -8x + 4$?
• What is the y-intercept of the function $f(x) = -8x + 4$?
• How do you find the x-intercept and y-intercept of a linear function?

Answer Key

• The x-intercept of the function $f(x) = -8x + 4$ is $(-0.5, 0)$.
• The y-intercept of the function $f(x) = -8x + 4$ is $(0, 4)$.

Explanation

To find the x-intercept of a linear function, we need to set $y = 0$ and solve for $x$. This can be done by substituting $y = 0$ into the equation and solving for $x$.

To find the y-intercept of a linear function, we need to set $x = 0$ and solve for $y$. This can be done by substituting $x = 0$ into the equation and solving for $y$.

Example

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

To find the x-intercept, we need to set $y = 0$ and solve for $x$. This can be done by substituting $y = 0$ into the equation and solving for $x$.

# Define the function
def f(x):
    return 2*x + 3

x_intercept = -f(0) / 2
print("The x-intercept is:", (x_intercept, 0))

When we run this code, we get the x-intercept as $(-1.5, 0)$.

To find the y-intercept, we need to set $x = 0$ and solve for $y$. This can be done by substituting $x = 0$ into the equation and solving for $y$.

# Define the function
def f(x):
    return 2*x + 3

y_intercept = f(0)
print("The y-intercept is:", (0, y_intercept))

When we run this code, we get the y-intercept as $(0, 3)$.

Conclusion

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In our previous article, we discussed the concept of intercepts of a linear function and how to find them. In this article, we will answer some frequently asked questions related to the intercepts of a linear function.

Q: What is the x-intercept of a linear function?

A: The x-intercept of a linear function is the point at which the function intersects the x-axis. It is the value of $x$ when $y = 0$.

Q: How do I find the x-intercept of a linear function?

A: To find the x-intercept of a linear function, you need to set $y = 0$ and solve for $x$. This can be done by substituting $y = 0$ into the equation and solving for $x$.

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

A: The y-intercept of a linear function is the point at which the function intersects the y-axis. It is the value of $y$ when $x = 0$.

Q: How do I find the y-intercept of a linear function?

A: To find the y-intercept of a linear function, you need to set $x = 0$ and solve for $y$. This can be done by substituting $x = 0$ into the equation and solving for $y$.

Q: Can you give an example of finding the x-intercept and y-intercept of a linear function?

A: Let's consider the function $f(x) = 2x + 3$. To find the x-intercept, we need to set $y = 0$ and solve for $x$.

# Define the function
def f(x):
    return 2*x + 3

x_intercept = -f(0) / 2
print("The x-intercept is:", (x_intercept, 0))

When we run this code, we get the x-intercept as $(-1.5, 0)$.

To find the y-intercept, we need to set $x = 0$ and solve for $y$.

# Define the function
def f(x):
    return 2*x + 3

y_intercept = f(0)
print("The y-intercept is:", (0, y_intercept))

When we run this code, we get the y-intercept as $(0, 3)$.

Q: What is the significance of the x-intercept and y-intercept of a linear function?

A: The x-intercept and y-intercept of a linear function are important because they help us understand the behavior of the function. The x-intercept tells us where the function intersects the x-axis, while the y-intercept tells us where the function intersects the y-axis.

Q: Can you give an example of a real-world application of the x-intercept and y-intercept of a linear function?

A: Let's consider a company that produces a product and sells it for a certain price. The cost of producing the product is $x$ dollars, and the revenue from selling the product is $y$ dollars. The profit is the difference between the revenue and the cost, which is given by the function $f(x) = 2x + 3$. In this case, the x-intercept represents the break-even point, where the revenue equals the cost. The y-intercept represents the maximum profit, which occurs when the revenue is maximized.

Conclusion

In conclusion, the x-intercept and y-intercept of a linear function are important concepts that help us understand the behavior of the function. By finding the x-intercept and y-intercept, we can gain insights into the behavior of the function and make informed decisions in real-world applications.

Discussion

• What is the x-intercept of a linear function?
• How do I find the x-intercept of a linear function?
• What is the y-intercept of a linear function?
• How do I find the y-intercept of a linear function?
• Can you give an example of finding the x-intercept and y-intercept of a linear function?
• What is the significance of the x-intercept and y-intercept of a linear function?
• Can you give an example of a real-world application of the x-intercept and y-intercept of a linear function?

Answer Key

• The x-intercept of a linear function is the point at which the function intersects the x-axis.
• To find the x-intercept of a linear function, you need to set $y = 0$ and solve for $x$.
• The y-intercept of a linear function is the point at which the function intersects the y-axis.
• To find the y-intercept of a linear function, you need to set $x = 0$ and solve for $y$.
• The x-intercept and y-intercept of a linear function are important concepts that help us understand the behavior of the function.
• The x-intercept and y-intercept of a linear function have real-world applications in fields such as business and economics.