15.2 Graphing Logarithmic Functions Answer Key
Are you struggling with graphing logarithmic functions? Not to worry, we've got you covered with this comprehensive answer key for 15.2 Graphing Logarithmic Functions.
Understanding Logarithmic Functions
Before we dive into graphing logarithmic functions, let's review what they are. Logarithmic functions are the inverse of exponential functions. They are used to solve equations where the variable is in the exponent. The general form of a logarithmic function is:
y = logbx
Where b is the base of the logarithm and x is the argument. The logarithm of a number tells you what exponent is needed to produce that number.
Graphing Logarithmic Functions
Graphing logarithmic functions can be a bit tricky, but with a few key steps, you'll be able to do it with ease. First, let's look at the general shape of a logarithmic function graph:
As you can see, the graph of a logarithmic function resembles an "S" shape. This is because logarithmic functions have asymptotes at x = 0 and y = 0. These asymptotes cause the graph to approach but never touch the axes.
Step 1: Determine the Domain and Range
The domain of a logarithmic function is all positive real numbers, since the logarithm of a negative number is undefined. The range of a logarithmic function is all real numbers. This is because the logarithm of 0 is undefined, but as x approaches 0, the logarithm approaches negative infinity, and as x approaches infinity, the logarithm approaches positive infinity.
Step 2: Find the Asymptotes
As we mentioned earlier, logarithmic functions have asymptotes at x = 0 and y = 0. To find these asymptotes, we set the argument or base of the logarithm equal to 0 and solve for x or y.
Step 3: Plot Points
To plot points on the graph of a logarithmic function, we can choose values of x and find the corresponding value of y using the logarithmic function. We can also choose values of y and find the corresponding value of x using the inverse logarithmic function.
Step 4: Sketch the Graph
Once we have a few points plotted, we can sketch the graph of the logarithmic function by connecting the points with a smooth curve. Remember to include the asymptotes in your graph.
Answer Key for 15.2 Graphing Logarithmic Functions
Now that we've covered the basics of graphing logarithmic functions, let's take a look at the answer key for 15.2 Graphing Logarithmic Functions. Below are the graphs for each of the functions:
1. y = log2(x)
2. y = log1/2(x)
3. y = -log3(x)
4. y = log4(x - 2)
5. y = -log1/3(x - 1) + 2
Conclusion
Graphing logarithmic functions can seem intimidating at first, but with practice and a good understanding of the key steps, you'll be able to master it in no time. Remember to determine the domain and range, find the asymptotes, plot points, and sketch the graph. And if you ever need help, refer back to this answer key for 15.2 Graphing Logarithmic Functions.
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