Which Comparison Is Correct For The Values Of F ( X F(x F ( X ] And G ( X G(x G ( X ] When X = − 1 X=-1 X = − 1 ?Function A : F ( X ) = − X 2 + 1 A: \, F(x)=-x^2+1 A : F ( X ) = − X 2 + 1 Function B B B : $[ \begin{array}{|l|l|} \hline x & G(x) \ \hline -3 & 7 \ \hline -1 & -4

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Introduction

When dealing with functions, it's essential to understand how to evaluate them at specific values of the input variable. In this article, we'll compare the values of two functions, $f(x)$ and $g(x)$, at $x=-1$. We'll examine the given functions, evaluate them at the specified value, and determine which comparison is correct.

Function $A$: $f(x)=-x^2+1$

The first function is given by the equation $f(x)=-x^2+1$. This is a quadratic function, which means it has a parabolic shape. To evaluate this function at $x=-1$, we substitute $x=-1$ into the equation:

$f(-1)=-(-1)^2+1$

Simplifying the Expression

To simplify the expression, we need to follow the order of operations (PEMDAS):

1. Evaluate the exponent: $(-1)^2=1$
2. Substitute the value into the equation: $f(-1)=-1+1$
3. Simplify the expression: $f(-1)=0$

Function $B$: $g(x)$

The second function is given by a table of values:

$x$	$g(x)$
-3	7
-1	-4

Evaluating $g(x)$ at $x=-1$

To evaluate $g(x)$ at $x=-1$, we look at the table and find the value of $g(x)$ when $x=-1$. According to the table, $g(-1)=-4$.

Comparison of $f(x)$ and $g(x)$ at $x=-1$

Now that we have evaluated both functions at $x=-1$, we can compare their values:

$f(-1)=0$ $g(-1)=-4$

Which Comparison is Correct?

Based on our evaluations, we can see that $f(-1)=0$ and $g(-1)=-4$. Therefore, the correct comparison is:

$f(-1) \neq g(-1)$

Conclusion

In this article, we compared the values of two functions, $f(x)$ and $g(x)$, at $x=-1$. We evaluated each function at the specified value and determined that $f(-1)=0$ and $g(-1)=-4$. This means that the correct comparison is $f(-1) \neq g(-1)$.

Understanding Function Evaluation

Evaluating functions at specific values is a crucial concept in mathematics. It allows us to determine the output of a function for a given input. In this article, we saw how to evaluate two functions, $f(x)$ and $g(x)$, at $x=-1$. We also compared their values and determined which comparison is correct.

Real-World Applications

Understanding function evaluation has many real-world applications. For example, in physics, we use functions to model the motion of objects. In economics, we use functions to model the behavior of markets. In computer science, we use functions to write efficient algorithms.

Tips for Evaluating Functions

When evaluating functions, it's essential to follow the order of operations (PEMDAS). This ensures that we simplify the expression correctly. Additionally, we should always check the table of values for functions that are given in tabular form.

Common Mistakes to Avoid

When evaluating functions, there are several common mistakes to avoid. One mistake is to forget to follow the order of operations (PEMDAS). Another mistake is to substitute the value into the equation incorrectly. Finally, we should always check the table of values for functions that are given in tabular form.

Conclusion

In conclusion, evaluating functions at specific values is a crucial concept in mathematics. We compared the values of two functions, $f(x)$ and $g(x)$, at $x=-1$ and determined which comparison is correct. We also discussed the importance of understanding function evaluation and provided tips for evaluating functions. By following these tips and avoiding common mistakes, we can become proficient in evaluating functions and apply this knowledge to real-world problems.

Introduction

In our previous article, we compared the values of two functions, $f(x)$ and $g(x)$, at $x=-1$. We evaluated each function at the specified value and determined that $f(-1)=0$ and $g(-1)=-4$. In this article, we'll answer some frequently asked questions about evaluating functions.

Q: What is the order of operations (PEMDAS)?

A: The order of operations (PEMDAS) is a set of rules that tells us which operations to perform first when simplifying an expression. The acronym PEMDAS stands for:

1. Parentheses: Evaluate expressions inside parentheses first.
2. Exponents: Evaluate any exponential expressions next (e.g., $2^3$).
3. Multiplication and Division: Evaluate any multiplication and division operations from left to right.
4. Addition and Subtraction: Finally, evaluate any addition and subtraction operations from left to right.

Q: How do I evaluate a function at a specific value?

A: To evaluate a function at a specific value, you need to substitute the value into the equation. For example, if we want to evaluate the function $f(x)=-x^2+1$ at $x=-1$, we would substitute $x=-1$ into the equation:

$f(-1)=-(-1)^2+1$

Q: What is the difference between a function and an equation?

A: A function is a relation between a set of inputs (called the domain) and a set of possible outputs (called the range). An equation, on the other hand, is a statement that says two expressions are equal. For example, the equation $x^2+3x-4=0$ is not a function, because it has multiple possible outputs for a given input.

Q: How do I determine if a function is even or odd?

A: To determine if a function is even or odd, you need to check if the function satisfies the following properties:

• Even function: $f(-x)=f(x)$ for all $x$ in the domain of the function.
• Odd function: $f(-x)=-f(x)$ for all $x$ in the domain of the function.

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

A: A linear function is a function of the form $f(x)=mx+b$, where $m$ and $b$ are constants. A quadratic function, on the other hand, is a function of the form $f(x)=ax^2+bx+c$, where $a$, $b$, and $c$ are constants.

Q: How do I graph a function?

A: To graph a function, you need to plot points on a coordinate plane. You can use a table of values or a graphing calculator to help you plot the points. Once you have plotted several points, you can draw a smooth curve through them to represent the function.

Q: What is the significance of the domain and range of a function?

A: The domain of a function is the set of all possible input values, while the range is the set of all possible output values. Understanding the domain and range of a function is crucial in many real-world applications, such as physics, engineering, and economics.

Conclusion

In this article, we answered some frequently asked questions about evaluating functions. We discussed the order of operations (PEMDAS), how to evaluate a function at a specific value, and the difference between a function and an equation. We also covered the properties of even and odd functions, linear and quadratic functions, and how to graph a function. By understanding these concepts, you can become proficient in evaluating functions and apply this knowledge to real-world problems.