If $f(x) = 5x - 2^3$, Find $f(-4)$.$f(-4) = [?]$

Introduction

In mathematics, functions are a fundamental concept that helps us describe relationships between variables. A function is a rule that assigns to each input, or value, a unique output. In this article, we will explore how to evaluate a function at a specific value, using the given function $f(x) = 5x - 2^3$ as an example.

Understanding the Function

Before we can evaluate the function at a specific value, we need to understand the function itself. The given function is $f(x) = 5x - 2^3$. This function takes an input value $x$ and returns an output value $f(x)$.

Evaluating the Function at a Specific Value

To evaluate the function at a specific value, we need to substitute the value into the function and simplify the expression. In this case, we want to find $f(-4)$.

Step 1: Substitute the Value into the Function

To find $f(-4)$, we need to substitute $x = -4$ into the function $f(x) = 5x - 2^3$. This gives us:

$$f(-4) = 5(-4) - 2^3$$

Step 2: Simplify the Expression

Now, we need to simplify the expression by evaluating the exponent and multiplying the coefficients.

$$f(-4) = -20 - 8$$

Step 3: Combine Like Terms

Finally, we need to combine the like terms to get the final answer.

$$f(-4) = -28$$

Conclusion

In this article, we learned how to evaluate a function at a specific value using the given function $f(x) = 5x - 2^3$ as an example. We followed a step-by-step process to substitute the value into the function, simplify the expression, and combine like terms to get the final answer.

Tips and Tricks

• When evaluating a function at a specific value, make sure to substitute the value into the function correctly.
• Simplify the expression by evaluating exponents and multiplying coefficients.
• Combine like terms to get the final answer.

Common Mistakes

• Failing to substitute the value into the function correctly.
• Not simplifying the expression by evaluating exponents and multiplying coefficients.
• Not combining like terms to get the final answer.

Real-World Applications

Evaluating functions is a fundamental concept in mathematics that has many real-world applications. For example, in physics, functions are used to describe the motion of objects, while in economics, functions are used to model the behavior of markets.

Practice Problems

1. Evaluate the function $f(x) = 2x + 3$ at $x = 5$.
2. Evaluate the function $f(x) = x^2 - 4$ at $x = 3$.
3. Evaluate the function $f(x) = \frac{x}{x + 1}$ at $x = 2$.

Solutions

1. $$f(5) = 2(5) + 3 = 13$$

2. $$f(3) = (3)^2 - 4 = 5$$

3. $$f(2) = \frac{2}{2 + 1} = \frac{2}{3}$$

Conclusion

Introduction

In our previous article, we explored how to evaluate a function at a specific value using the given function $f(x) = 5x - 2^3$ as an example. In this article, we will answer some frequently asked questions about evaluating functions.

Q&A

Q: What is the difference between evaluating a function and finding the value of a function?

A: Evaluating a function means finding the value of the function at a specific input value, while finding the value of a function means finding the value of the function for all possible input values.

Q: How do I know if a function is defined at a specific value?

A: A function is defined at a specific value if the function is continuous at that value. In other words, if the function has no holes or jumps at that value.

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

A: A function is a rule that assigns to each input value a unique output value, while an equation is a statement that two expressions are equal.

Q: Can I evaluate a function at a value that is not in the domain of the function?

A: No, you cannot evaluate a function at a value that is not in the domain of the function. The domain of a function is the set of all possible input values for which the function is defined.

Q: How do I evaluate a function with multiple variables?

A: To evaluate a function with multiple variables, you need to substitute the values of all the variables into the function and simplify the expression.

Q: Can I use a calculator to evaluate a function?

A: Yes, you can use a calculator to evaluate a function. However, make sure to enter the function and the input value correctly.

Q: What is the difference between evaluating a function and graphing a function?

A: Evaluating a function means finding the value of the function at a specific input value, while graphing a function means visualizing the function on a coordinate plane.

Q: Can I evaluate a function with a variable in the exponent?

A: Yes, you can evaluate a function with a variable in the exponent. However, make sure to follow the order of operations and simplify the expression correctly.

Q: How do I evaluate a function with a negative exponent?

A: To evaluate a function with a negative exponent, you need to rewrite the exponent as a positive exponent and then simplify the expression.

Q: Can I evaluate a function with a fraction as an input value?

A: Yes, you can evaluate a function with a fraction as an input value. However, make sure to simplify the fraction correctly before substituting it into the function.

Q: What is the difference between evaluating a function and finding the derivative of a function?

A: Evaluating a function means finding the value of the function at a specific input value, while finding the derivative of a function means finding the rate of change of the function with respect to the input value.

Conclusion

In this article, we answered some frequently asked questions about evaluating functions. We discussed the difference between evaluating a function and finding the value of a function, the difference between a function and an equation, and how to evaluate a function with multiple variables. We also discussed how to use a calculator to evaluate a function and the difference between evaluating a function and graphing a function.

Practice Problems

1. Evaluate the function $f(x) = 2x + 3$ at $x = 5$.
2. Evaluate the function $f(x) = x^2 - 4$ at $x = 3$.
3. Evaluate the function $f(x) = \frac{x}{x + 1}$ at $x = 2$.

Solutions

1. $$f(5) = 2(5) + 3 = 13$$

2. $$f(3) = (3)^2 - 4 = 5$$

3. $$f(2) = \frac{2}{2 + 1} = \frac{2}{3}$$

Conclusion

In this article, we learned how to evaluate a function at a specific value using the given function $f(x) = 5x - 2^3$ as an example. We also answered some frequently asked questions about evaluating functions and provided practice problems to help you improve your skills.