Graph The Function: \[$ F(x) = 0.5x - 3 \$\]Step 1: Calculate The Initial Value Of The Function.$\[ F(0) = -3 \\]Step 2: Plot The Initial Value Of The Function At The Point (0, -3).Step 3: Evaluate The Function At Two More

by ADMIN 223 views

Introduction

Graphing a function is an essential skill in mathematics, and it's used in various fields such as science, engineering, and economics. In this article, we will graph the function f(x) = 0.5x - 3 using a step-by-step approach. We will start by calculating the initial value of the function, then plot the initial value on a coordinate plane, and finally evaluate the function at two more points.

Step 1: Calculate the Initial Value of the Function

The initial value of a function is the value of the function at x = 0. To calculate the initial value of the function f(x) = 0.5x - 3, we substitute x = 0 into the function.

f(0)=0.5(0)−3{ f(0) = 0.5(0) - 3 }

Using the order of operations, we first multiply 0.5 and 0, which equals 0. Then, we subtract 3 from 0.

f(0)=0−3{ f(0) = 0 - 3 }

f(0)=−3{ f(0) = -3 }

So, the initial value of the function f(x) = 0.5x - 3 is -3.

Step 2: Plot the Initial Value of the Function at the Point (0, -3)

To plot the initial value of the function at the point (0, -3), we need to understand the concept of a coordinate plane. A coordinate plane is a two-dimensional plane that has two axes: the x-axis and the y-axis. The x-axis represents the horizontal direction, and the y-axis represents the vertical direction.

To plot the point (0, -3), we start at the origin (0, 0) and move 3 units down on the y-axis. This will bring us to the point (0, -3).

Step 3: Evaluate the Function at Two More Points

Now that we have plotted the initial value of the function at the point (0, -3), we need to evaluate the function at two more points. Let's choose x = 2 and x = 4.

For x = 2, we substitute x = 2 into the function f(x) = 0.5x - 3.

f(2)=0.5(2)−3{ f(2) = 0.5(2) - 3 }

Using the order of operations, we first multiply 0.5 and 2, which equals 1. Then, we subtract 3 from 1.

f(2)=1−3{ f(2) = 1 - 3 }

f(2)=−2{ f(2) = -2 }

So, the value of the function at x = 2 is -2.

For x = 4, we substitute x = 4 into the function f(x) = 0.5x - 3.

f(4)=0.5(4)−3{ f(4) = 0.5(4) - 3 }

Using the order of operations, we first multiply 0.5 and 4, which equals 2. Then, we subtract 3 from 2.

f(4)=2−3{ f(4) = 2 - 3 }

f(4)=−1{ f(4) = -1 }

So, the value of the function at x = 4 is -1.

Plotting the Function

Now that we have evaluated the function at three points, we can plot the function on a coordinate plane. We will plot the points (0, -3), (2, -2), and (4, -1) on the coordinate plane.

Discussion

Graphing a function is an essential skill in mathematics, and it's used in various fields such as science, engineering, and economics. In this article, we graphed the function f(x) = 0.5x - 3 using a step-by-step approach. We calculated the initial value of the function, plotted the initial value on a coordinate plane, and evaluated the function at two more points.

Conclusion

Graphing a function is a powerful tool that allows us to visualize the behavior of a function. By following the steps outlined in this article, we can graph a function and gain a deeper understanding of its behavior. Whether you're a student, a teacher, or a professional, graphing a function is an essential skill that can help you solve problems and make informed decisions.

Additional Resources

If you're interested in learning more about graphing functions, here are some additional resources that you may find helpful:

  • Khan Academy: Graphing Functions
  • Mathway: Graphing Functions
  • Wolfram Alpha: Graphing Functions

Frequently Asked Questions

Q: What is the initial value of the function f(x) = 0.5x - 3? A: The initial value of the function f(x) = 0.5x - 3 is -3.

Q: How do I plot the initial value of the function on a coordinate plane? A: To plot the initial value of the function on a coordinate plane, start at the origin (0, 0) and move 3 units down on the y-axis.

Q: How do I evaluate the function at two more points? A: To evaluate the function at two more points, substitute the x-values into the function and simplify the expression.

Q: What is the value of the function at x = 2? A: The value of the function at x = 2 is -2.

Introduction

Graphing a function is an essential skill in mathematics, and it's used in various fields such as science, engineering, and economics. In our previous article, we graphed the function f(x) = 0.5x - 3 using a step-by-step approach. In this article, we will answer some frequently asked questions about graphing functions.

Q&A

Q: What is the initial value of the function f(x) = 0.5x - 3?

A: The initial value of the function f(x) = 0.5x - 3 is -3. This is the value of the function at x = 0.

Q: How do I plot the initial value of the function on a coordinate plane?

A: To plot the initial value of the function on a coordinate plane, start at the origin (0, 0) and move 3 units down on the y-axis. This will bring you to the point (0, -3).

Q: How do I evaluate the function at two more points?

A: To evaluate the function at two more points, substitute the x-values into the function and simplify the expression. For example, to evaluate the function at x = 2, substitute x = 2 into the function f(x) = 0.5x - 3.

Q: What is the value of the function at x = 2?

A: The value of the function at x = 2 is -2. This is calculated by substituting x = 2 into the function f(x) = 0.5x - 3.

Q: What is the value of the function at x = 4?

A: The value of the function at x = 4 is -1. This is calculated by substituting x = 4 into the function f(x) = 0.5x - 3.

Q: How do I graph a function on a coordinate plane?

A: To graph a function on a coordinate plane, start by plotting the initial value of the function. Then, evaluate the function at two more points and plot those points on the coordinate plane. Finally, draw a line through the points to graph the function.

Q: What is the difference between a function and a relation?

A: A function is a relation between a set of inputs (called the domain) and a set of possible outputs (called the range). A relation is a set of ordered pairs that satisfy a certain condition. Not all relations are functions.

Q: How do I determine if a relation is a function?

A: To determine if a relation is a function, check if each input has only one output. If each input has only one output, then the relation is a function.

Q: What is the domain of a function?

A: The domain of a function is the set of all possible inputs (x-values) that the function can accept. For example, the domain of the function f(x) = 1/x is all real numbers except 0.

Q: What is the range of a function?

A: The range of a function is the set of all possible outputs (y-values) that the function can produce. For example, the range of the function f(x) = 1/x is all real numbers except 0.

Conclusion

Graphing a function is an essential skill in mathematics, and it's used in various fields such as science, engineering, and economics. In this article, we answered some frequently asked questions about graphing functions. We hope that this article has been helpful in clarifying any confusion you may have had about graphing functions.

Additional Resources

If you're interested in learning more about graphing functions, here are some additional resources that you may find helpful:

  • Khan Academy: Graphing Functions
  • Mathway: Graphing Functions
  • Wolfram Alpha: Graphing Functions

Frequently Asked Questions

Q: What is the initial value of the function f(x) = 0.5x - 3? A: The initial value of the function f(x) = 0.5x - 3 is -3.

Q: How do I plot the initial value of the function on a coordinate plane? A: To plot the initial value of the function on a coordinate plane, start at the origin (0, 0) and move 3 units down on the y-axis.

Q: How do I evaluate the function at two more points? A: To evaluate the function at two more points, substitute the x-values into the function and simplify the expression.

Q: What is the value of the function at x = 2? A: The value of the function at x = 2 is -2.

Q: What is the value of the function at x = 4? A: The value of the function at x = 4 is -1.

Q: How do I graph a function on a coordinate plane? A: To graph a function on a coordinate plane, start by plotting the initial value of the function. Then, evaluate the function at two more points and plot those points on the coordinate plane. Finally, draw a line through the points to graph the function.

Q: What is the difference between a function and a relation? A: A function is a relation between a set of inputs (called the domain) and a set of possible outputs (called the range). A relation is a set of ordered pairs that satisfy a certain condition. Not all relations are functions.

Q: How do I determine if a relation is a function? A: To determine if a relation is a function, check if each input has only one output. If each input has only one output, then the relation is a function.

Q: What is the domain of a function? A: The domain of a function is the set of all possible inputs (x-values) that the function can accept. For example, the domain of the function f(x) = 1/x is all real numbers except 0.

Q: What is the range of a function? A: The range of a function is the set of all possible outputs (y-values) that the function can produce. For example, the range of the function f(x) = 1/x is all real numbers except 0.