Evaluate $f(x)=\frac{5}{2x+8}$ When $x=-4$.A. Undefined B. 5 C. $\frac{5}{16}$ D. 0
Introduction
In mathematics, evaluating a function at a specific value of the variable is a crucial concept in understanding the behavior of the function. In this article, we will evaluate the function $f(x)=\frac{5}{2x+8}$ at $x=-4$. This involves substituting the value of $x$ into the function and simplifying the expression to obtain the final result.
Understanding the Function
The given function is $f(x)=\frac{5}{2x+8}$. This is a rational function, which means it is the ratio of two polynomials. The numerator is a constant, 5, while the denominator is a linear expression, $2x+8$. To evaluate the function at $x=-4$, we need to substitute $x=-4$ into the function and simplify the expression.
Substituting $x=-4$ into the Function
To evaluate the function at $x=-4$, we substitute $x=-4$ into the function:
Simplifying the Expression
Now, we simplify the expression by evaluating the denominator:
Evaluating the Function at $x=-4$
Since the denominator is equal to 0, the function is undefined at $x=-4$. This is because division by zero is undefined in mathematics.
Conclusion
In conclusion, the function $f(x)=\frac{5}{2x+8}$ is undefined at $x=-4$. This is because the denominator is equal to 0, which makes the function undefined.
Final Answer
The final answer is A. undefined.
Why is the Function Undefined?
The function is undefined at $x=-4$ because the denominator is equal to 0. This is a critical concept in mathematics, as division by zero is undefined. In this case, the function is undefined at $x=-4$, which means that the function does not have a value at this point.
What Happens When the Denominator is Equal to 0?
When the denominator is equal to 0, the function is undefined. This is because division by zero is undefined in mathematics. In this case, the function $f(x)=\frac{5}{2x+8}$ is undefined at $x=-4$ because the denominator is equal to 0.
Importance of Understanding Function Evaluation
Understanding function evaluation is crucial in mathematics, as it helps us understand the behavior of functions. In this article, we evaluated the function $f(x)=\frac{5}{2x+8}$ at $x=-4$. This involved substituting the value of $x$ into the function and simplifying the expression to obtain the final result. By understanding function evaluation, we can better understand the behavior of functions and make informed decisions in mathematics and other fields.
Real-World Applications of Function Evaluation
Function evaluation has numerous real-world applications. For example, in physics, function evaluation is used to model the motion of objects. In economics, function evaluation is used to model the behavior of economic systems. In computer science, function evaluation is used to model the behavior of algorithms. By understanding function evaluation, we can better understand the behavior of complex systems and make informed decisions in various fields.
Common Mistakes in Function Evaluation
There are several common mistakes that people make when evaluating functions. One common mistake is to forget to simplify the expression. Another common mistake is to forget to check if the denominator is equal to 0. By understanding function evaluation and avoiding these common mistakes, we can ensure that our results are accurate and reliable.
Tips for Evaluating Functions
Here are some tips for evaluating functions:
- Always simplify the expression before evaluating the function.
- Always check if the denominator is equal to 0 before evaluating the function.
- Use a calculator or computer software to evaluate functions, especially for complex expressions.
- Read the problem carefully and understand what is being asked.
- Check your work and make sure that your results are accurate and reliable.
Conclusion
In conclusion, evaluating the function $f(x)=\frac{5}{2x+8}$ at $x=-4$ involves substituting the value of $x$ into the function and simplifying the expression. By understanding function evaluation, we can better understand the behavior of functions and make informed decisions in mathematics and other fields.