Given The Functions \[$ G(x) = 3(x - 1) \$\] And \[$ H(x) = 0.25x - 13 \$\]:1. Find \[$ G(10) \$\].2. Find \[$ G(-6) \$\].3. Find \[$ H(12) \$\].4. Find \[$ H(5) \$\].For The Following, Use The Same

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Introduction

In mathematics, functions are used to describe relationships between variables. Evaluating functions involves substituting specific values into the function and calculating the resulting output. In this article, we will explore how to evaluate two given functions, g(x) and h(x), at specific values of x.

Function g(x)

The first function is given by the equation:

g(x)=3(x−1) g(x) = 3(x - 1)

This function takes an input value x, subtracts 1 from it, and then multiplies the result by 3.

Evaluating g(10)

To evaluate g(10), we substitute x = 10 into the function g(x):

g(10)=3(10−1) g(10) = 3(10 - 1)

Using the order of operations, we first subtract 1 from 10, which gives us 9. Then, we multiply 9 by 3, which gives us 27.

g(10)=27 g(10) = 27

Evaluating g(-6)

To evaluate g(-6), we substitute x = -6 into the function g(x):

g(−6)=3(−6−1) g(-6) = 3(-6 - 1)

Using the order of operations, we first subtract 1 from -6, which gives us -7. Then, we multiply -7 by 3, which gives us -21.

g(−6)=−21 g(-6) = -21

Function h(x)

The second function is given by the equation:

h(x)=0.25x−13 h(x) = 0.25x - 13

This function takes an input value x, multiplies it by 0.25, and then subtracts 13 from the result.

Evaluating h(12)

To evaluate h(12), we substitute x = 12 into the function h(x):

h(12)=0.25(12)−13 h(12) = 0.25(12) - 13

Using the order of operations, we first multiply 12 by 0.25, which gives us 3. Then, we subtract 13 from 3, which gives us -10.

h(12)=−10 h(12) = -10

Evaluating h(5)

To evaluate h(5), we substitute x = 5 into the function h(x):

h(5)=0.25(5)−13 h(5) = 0.25(5) - 13

Using the order of operations, we first multiply 5 by 0.25, which gives us 1.25. Then, we subtract 13 from 1.25, which gives us -11.75.

h(5)=−11.75 h(5) = -11.75

Conclusion

In this article, we evaluated two given functions, g(x) and h(x), at specific values of x. We used the order of operations to simplify the expressions and calculate the resulting outputs. By following these steps, we can evaluate functions and understand the relationships between variables.

Key Takeaways

  • To evaluate a function, substitute the input value into the function and calculate the resulting output.
  • Use the order of operations to simplify the expression and calculate the result.
  • Functions can be used to describe relationships between variables and can be evaluated at specific values of x.

Further Reading

For more information on functions and evaluating expressions, see the following resources:

Introduction

In our previous article, we explored how to evaluate two given functions, g(x) and h(x), at specific values of x. In this article, we will answer some frequently asked questions about evaluating functions.

Q: What is the order of operations when evaluating a function?

A: The order of operations when evaluating a function is:

  1. Parentheses: Evaluate expressions inside parentheses first.
  2. Exponents: Evaluate any exponential expressions next.
  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 know which function to use when evaluating an expression?

A: When evaluating an expression, you need to determine which function to use based on the input value. For example, if you are given the expression g(x) = 3(x - 1) and you want to evaluate it at x = 10, you would substitute x = 10 into the function g(x).

Q: What if I have a function with multiple variables? How do I evaluate it?

A: If you have a function with multiple variables, you need to substitute the input values into the function and calculate the resulting output. For example, if you have a function f(x, y) = 2x + 3y and you want to evaluate it at x = 2 and y = 3, you would substitute x = 2 and y = 3 into the function f(x, y).

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

A: Yes, you can use a calculator to evaluate a function. In fact, calculators are often used to evaluate complex functions quickly and accurately. However, it's always a good idea to double-check your work by hand to ensure that you understand the underlying math.

Q: What if I make a mistake when evaluating a function? How do I fix it?

A: If you make a mistake when evaluating a function, don't worry! It's easy to fix. First, identify the mistake and correct it. Then, re-evaluate the function using the corrected input values. If you're still having trouble, try breaking down the function into smaller parts and evaluating each part separately.

Q: Are there any special cases I should be aware of when evaluating functions?

A: Yes, there are several special cases you should be aware of when evaluating functions. For example:

  • If the input value is a fraction, you may need to simplify the fraction before evaluating the function.
  • If the input value is a decimal, you may need to round the decimal to a specific number of places before evaluating the function.
  • If the function has a variable with a negative exponent, you may need to use the rule for negative exponents to simplify the expression.

Q: Can I use technology to help me evaluate functions?

A: Yes, there are many tools and resources available to help you evaluate functions. For example:

  • Graphing calculators: These can help you visualize the function and evaluate it at specific points.
  • Online function evaluators: These can help you evaluate functions quickly and accurately.
  • Math software: This can help you evaluate functions and perform other mathematical operations.

Conclusion

In this article, we answered some frequently asked questions about evaluating functions. We covered topics such as the order of operations, how to determine which function to use, and how to evaluate functions with multiple variables. We also discussed special cases and how to use technology to help you evaluate functions.

Key Takeaways

  • The order of operations is: parentheses, exponents, multiplication and division, and addition and subtraction.
  • You need to determine which function to use based on the input value.
  • You can use a calculator to evaluate a function, but it's always a good idea to double-check your work by hand.
  • There are several special cases you should be aware of when evaluating functions, such as fractions, decimals, and negative exponents.
  • You can use technology to help you evaluate functions, such as graphing calculators, online function evaluators, and math software.

Further Reading

For more information on evaluating functions, see the following resources: