Graph The Function F ( X ) = Log ⁡ 2 X − 1 F(x) = \log_2 X - 1 F ( X ) = Lo G 2 ​ X − 1 On The Axes Below. You Must Plot The Asymptote And Any Two Points With Integer Coordinates.Asymptote:

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Introduction

Graphing a function involves plotting its corresponding points on a coordinate plane. In this case, we are given the function $f(x) = \log_2 x - 1$. To graph this function, we need to find its asymptote and two points with integer coordinates.

Understanding the Function

The given function is a logarithmic function with base 2. The general form of a logarithmic function is $f(x) = \log_b x$, where $b$ is the base of the logarithm. In this case, the base is 2. The function $f(x) = \log_2 x - 1$ can be rewritten as $f(x) = \log_2 x - \log_2 2$, which simplifies to $f(x) = \log_2 \frac{x}{2}$.

Finding the Asymptote

The asymptote of a logarithmic function is the horizontal line that the function approaches as $x$ approaches infinity. In the case of the function $f(x) = \log_2 x - 1$, the asymptote is the line $y = -1$.

Plotting Two Points with Integer Coordinates

To plot two points with integer coordinates, we need to find the values of $x$ and $y$ that satisfy the equation $f(x) = \log_2 x - 1$. We can choose two values of $x$ that are easy to work with, such as $x = 2$ and $x = 4$.

For $x = 2$, we have:

$$f(2) = \log_2 2 - 1 = 0 - 1 = -1$$

So, the point $(2, -1)$ lies on the graph of the function.

For $x = 4$, we have:

$$f(4) = \log_2 4 - 1 = 2 - 1 = 1$$

So, the point $(4, 1)$ lies on the graph of the function.

Graphing the Function

Now that we have found the asymptote and two points with integer coordinates, we can graph the function $f(x) = \log_2 x - 1$. The graph will be a curve that approaches the asymptote $y = -1$ as $x$ approaches infinity.

Conclusion

In this article, we graphed the function $f(x) = \log_2 x - 1$ on the given axes. We found the asymptote and two points with integer coordinates, and used this information to graph the function. The graph of the function is a curve that approaches the asymptote $y = -1$ as $x$ approaches infinity.

Asymptote

The asymptote of the function $f(x) = \log_2 x - 1$ is the line $y = -1$.

Discussion

The graph of the function $f(x) = \log_2 x - 1$ is a curve that approaches the asymptote $y = -1$ as $x$ approaches infinity. This is because the logarithmic function grows slowly as $x$ increases, and the constant term $-1$ shifts the graph down by one unit.

Mathematical Analysis

The function $f(x) = \log_2 x - 1$ can be analyzed mathematically using the properties of logarithmic functions. The logarithmic function is defined for all positive real numbers, and the constant term $-1$ shifts the graph down by one unit.

Graphical Analysis

The graph of the function $f(x) = \log_2 x - 1$ can be analyzed graphically by plotting the function on a coordinate plane. The graph will be a curve that approaches the asymptote $y = -1$ as $x$ approaches infinity.

Conclusion

In conclusion, the graph of the function $f(x) = \log_2 x - 1$ is a curve that approaches the asymptote $y = -1$ as $x$ approaches infinity. The function can be analyzed mathematically using the properties of logarithmic functions, and graphically by plotting the function on a coordinate plane.

References

• [1] "Logarithmic Functions" by Math Open Reference
• [2] "Graphing Logarithmic Functions" by Purplemath

Keywords

• Logarithmic function
• Asymptote
• Graphing
• Integer coordinates
• Mathematical analysis
• Graphical analysis
  Q&A: Graphing the Function $f(x) = \log_2 x - 1$ =====================================================

Introduction

In our previous article, we graphed the function $f(x) = \log_2 x - 1$ on the given axes. We found the asymptote and two points with integer coordinates, and used this information to graph the function. In this article, we will answer some frequently asked questions about graphing the function $f(x) = \log_2 x - 1$.

Q: What is the asymptote of the function $f(x) = \log_2 x - 1$?

A: The asymptote of the function $f(x) = \log_2 x - 1$ is the line $y = -1$.

Q: How do I find the asymptote of a logarithmic function?

A: To find the asymptote of a logarithmic function, you need to look at the general form of the function, which is $f(x) = \log_b x$. The asymptote is the horizontal line that the function approaches as $x$ approaches infinity.

Q: What are the two points with integer coordinates that lie on the graph of the function $f(x) = \log_2 x - 1$?

A: The two points with integer coordinates that lie on the graph of the function $f(x) = \log_2 x - 1$ are $(2, -1)$ and $(4, 1)$.

Q: How do I graph a logarithmic function?

A: To graph a logarithmic function, you need to find the asymptote and two points with integer coordinates. Then, you can use this information to graph the function.

Q: What is the domain of the function $f(x) = \log_2 x - 1$?

A: The domain of the function $f(x) = \log_2 x - 1$ is all positive real numbers.

Q: What is the range of the function $f(x) = \log_2 x - 1$?

A: The range of the function $f(x) = \log_2 x - 1$ is all real numbers.

Q: How do I analyze a logarithmic function mathematically?

A: To analyze a logarithmic function mathematically, you need to use the properties of logarithmic functions. You can use the fact that the logarithmic function is defined for all positive real numbers, and that the constant term shifts the graph down by one unit.

Q: How do I analyze a logarithmic function graphically?

A: To analyze a logarithmic function graphically, you need to plot the function on a coordinate plane. The graph will be a curve that approaches the asymptote as $x$ approaches infinity.

Conclusion

In conclusion, graphing the function $f(x) = \log_2 x - 1$ involves finding the asymptote and two points with integer coordinates, and using this information to graph the function. We hope that this Q&A article has been helpful in answering some of the frequently asked questions about graphing the function $f(x) = \log_2 x - 1$.

References

• [1] "Logarithmic Functions" by Math Open Reference
• [2] "Graphing Logarithmic Functions" by Purplemath

Keywords

• Logarithmic function
• Asymptote
• Graphing
• Integer coordinates
• Mathematical analysis
• Graphical analysis
• Domain
• Range