Algebra and Trigonometry (6th Edition)
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN: 9780134463216
Author: Robert F. Blitzer
Publisher: PEARSON
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**Transcription and Explanation for Educational Website** --- **Graph and Equation Matching Exercise** The image presents a set of graphs and equations designed to test your understanding of mathematical functions and their graphical representations. Below are the components of the image: ### Graphs There are four graphs, each represented by a different color: - **Blue Graph:** This graph is likely an exponential function showing growth as it moves from left to right. - **Red Graph:** This graph appears to be another exponential function or a related logarithmic function but differs in behavior from the blue graph. - **Black Graph:** This graph exhibits characteristics of either an exponential function or a logarithmic function with a specific base. - **Green Graph:** This graph typically represents a logarithmic function. ### Task You are tasked with matching each equation to its corresponding graph: 1. \(10^x\) 2. \(\log(x)\) 3. \(e^x\) 4. \(\ln(x)\) ### Options - a. blue - b. red - c. black - d. green Use the dropdown menu next to each equation to select the color of the graph that correctly represents it. This exercise will test your understanding of how exponential and logarithmic functions behave visually. **Note:** Understanding the standard shapes of these functions will assist in matching them to the appropriate graphs. For instance, exponential functions generally curve upwards, while logarithmic functions increase slowly and may appear as a gradual curve. Consider the axes, intercepts, and behavior of the function as \(x\) approaches infinity or zero when making your selections.
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Transcribed Image Text:**Transcription and Explanation for Educational Website** --- **Graph and Equation Matching Exercise** The image presents a set of graphs and equations designed to test your understanding of mathematical functions and their graphical representations. Below are the components of the image: ### Graphs There are four graphs, each represented by a different color: - **Blue Graph:** This graph is likely an exponential function showing growth as it moves from left to right. - **Red Graph:** This graph appears to be another exponential function or a related logarithmic function but differs in behavior from the blue graph. - **Black Graph:** This graph exhibits characteristics of either an exponential function or a logarithmic function with a specific base. - **Green Graph:** This graph typically represents a logarithmic function. ### Task You are tasked with matching each equation to its corresponding graph: 1. \(10^x\) 2. \(\log(x)\) 3. \(e^x\) 4. \(\ln(x)\) ### Options - a. blue - b. red - c. black - d. green Use the dropdown menu next to each equation to select the color of the graph that correctly represents it. This exercise will test your understanding of how exponential and logarithmic functions behave visually. **Note:** Understanding the standard shapes of these functions will assist in matching them to the appropriate graphs. For instance, exponential functions generally curve upwards, while logarithmic functions increase slowly and may appear as a gradual curve. Consider the axes, intercepts, and behavior of the function as \(x\) approaches infinity or zero when making your selections.
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