What Is The Output Value Of The Given Function When The Input Value Is 4?$\[ Y = 10x + 9 \\]Input: \[$ X = 4 \$\] Output: \[$(4, \, [?])\$\]
Introduction
In mathematics, functions are used to describe the relationship between input and output values. A function is a rule that assigns to each input value, or input, exactly one output value, or output. In this article, we will explore the output value of a given function when the input value is 4.
The Function
The given function is y = 10x + 9, where x is the input value and y is the output value. This is a linear function, which means that the output value is directly proportional to the input value.
Input Value
The input value is given as x = 4. This is the value that we will use to find the output value of the function.
Finding the Output Value
To find the output value, we need to substitute the input value into the function. This means that we will replace x with 4 in the equation y = 10x + 9.
Substituting the Input Value
y = 10x + 9 y = 10(4) + 9 y = 40 + 9 y = 49
Conclusion
Therefore, the output value of the given function when the input value is 4 is 49.
Understanding the Function
The function y = 10x + 9 is a linear function, which means that the output value is directly proportional to the input value. This means that if we increase the input value, the output value will also increase. In this case, when the input value is 4, the output value is 49.
Graphing the Function
To visualize the function, we can graph it on a coordinate plane. The graph of the function y = 10x + 9 is a straight line with a slope of 10 and a y-intercept of 9.
Properties of the Function
The function y = 10x + 9 has several properties that are important to understand. These properties include:
- Domain: The domain of the function is all real numbers, which means that the input value can be any real number.
- Range: The range of the function is all real numbers greater than or equal to 9, which means that the output value can be any real number greater than or equal to 9.
- Slope: The slope of the function is 10, which means that the output value increases by 10 for every 1 increase in the input value.
- Y-intercept: The y-intercept of the function is 9, which means that the output value is 9 when the input value is 0.
Applications of the Function
The function y = 10x + 9 has several applications in real-world scenarios. These applications include:
- Cost and Revenue: The function can be used to model the cost and revenue of a business. For example, if the cost of producing x units of a product is 10x + 9, then the revenue from selling x units of the product is 10x + 9.
- Distance and Time: The function can be used to model the distance and time of an object moving at a constant speed. For example, if an object is moving at a speed of 10 units per second, then the distance traveled in t seconds is 10t + 9.
- Temperature and Time: The function can be used to model the temperature and time of a system. For example, if the temperature of a system is increasing at a rate of 10 degrees per hour, then the temperature after t hours is 10t + 9.
Conclusion
In conclusion, the output value of the given function when the input value is 4 is 49. The function y = 10x + 9 is a linear function that has several properties and applications in real-world scenarios. Understanding the function and its properties is important for modeling and solving problems in mathematics and other fields.
Introduction
In the previous article, we explored the output value of the function y = 10x + 9 when the input value is 4. In this article, we will answer some frequently asked questions (FAQs) about the function.
Q: What is the domain of the function y = 10x + 9?
A: The domain of the function y = 10x + 9 is all real numbers, which means that the input value can be any real number.
Q: What is the range of the function y = 10x + 9?
A: The range of the function y = 10x + 9 is all real numbers greater than or equal to 9, which means that the output value can be any real number greater than or equal to 9.
Q: What is the slope of the function y = 10x + 9?
A: The slope of the function y = 10x + 9 is 10, which means that the output value increases by 10 for every 1 increase in the input value.
Q: What is the y-intercept of the function y = 10x + 9?
A: The y-intercept of the function y = 10x + 9 is 9, which means that the output value is 9 when the input value is 0.
Q: How do I graph the function y = 10x + 9?
A: To graph the function y = 10x + 9, you can use a coordinate plane and plot the points (0, 9) and (1, 19). Then, draw a straight line through these points to get the graph of the function.
Q: Can I use the function y = 10x + 9 to model real-world scenarios?
A: Yes, the function y = 10x + 9 can be used to model real-world scenarios such as cost and revenue, distance and time, and temperature and time.
Q: How do I find the output value of the function y = 10x + 9 when the input value is not 4?
A: To find the output value of the function y = 10x + 9 when the input value is not 4, you can substitute the input value into the function and solve for the output value.
Q: Can I use the function y = 10x + 9 to solve equations?
A: Yes, the function y = 10x + 9 can be used to solve equations. For example, if the equation is 10x + 9 = 49, you can substitute the value of y into the function and solve for x.
Q: How do I determine if the function y = 10x + 9 is a linear function?
A: To determine if the function y = 10x + 9 is a linear function, you can check if the output value is directly proportional to the input value. If the output value increases by a constant amount for every 1 increase in the input value, then the function is a linear function.
Q: Can I use the function y = 10x + 9 to model exponential growth or decay?
A: No, the function y = 10x + 9 is a linear function and cannot be used to model exponential growth or decay.
Conclusion
In conclusion, the function y = 10x + 9 is a linear function that has several properties and applications in real-world scenarios. Understanding the function and its properties is important for modeling and solving problems in mathematics and other fields.