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Match the formula of the exponential function to its graph. Graphs of Exponential Functions 5 4 3 2 1 -5 -4 -3 -2 -1 > -1 -2 -3 -4 -5 2 3 4 5 Formulas for the Graphs a. f(x) = (²)* 2 b. f(x) = c. f(x) = 2x d. f(x) = = - (²) 2 - (22)

Match the formula of the exponential function to its graph. Graphs of Exponential Functions 5 4 3 2 1 -5 -4 -3 -2 -1 > -1 -2 -3 -4 -5 2 3 4 5 Formulas for the Graphs a. f(x) = (²)* 2 b. f(x) = c. f(x) = 2x d. f(x) = = - (²) 2 - (22)

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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**Match the formula of the exponential function to its graph.** ### Graphs of Exponential Functions Below are graphs of four different exponential functions. Your task is to match each graph to the correct formula from the list provided. 1. **Graph 1:** - **Description:** This graph shows a curve that starts from the top left quadrant, gradually decreases as it moves to the right, and approaches the x-axis without touching it. - **Graph Position:** First graph from the top. 2. **Graph 2:** - **Description:** This graph shows a curve that starts low at the left side, gradually increases, and steeply rises as it moves towards the right. - **Graph Position:** Second graph from the top. 3. **Graph 3:** - **Description:** This graph is the reflection of the first graph across the x-axis, decreasing exponentially into the negative y-values as it moves to the right. - **Graph Position:** Third graph from the top. 4. **Graph 4:** - **Description:** This graph is similar to the second graph but it stays in the negative y-values and decreases exponentially as it moves to the left. - **Graph Position:** Fourth graph from the top. ### Formulas for the Graphs a. \( f(x) = \left( \frac{1}{2} \right)^x \) b. \( f(x) = -\left( \frac{1}{2} \right)^x \) c. \( f(x) = 2^x \) d. \( f(x) = -(2^x) \) ### Matching Match each graph with the corresponding formula: 1. **Graph 1**: \( f(x) = \left( \frac{1}{2} \right)^x \) 2. **Graph 2**: \( f(x) = 2^x \) 3. **Graph 3**: \( f(x) = -\left( \frac{1}{2} \right)^x \) 4. **Graph 4**: \( f(x) = -(2^x) \) **Explanation for Appropriate Matching:** - **Graph 1** (a): Exponential decay, \( \left( \frac{1}{2} \right)^x \) shows the function decreasing as x increases, approaching zero. - **Graph
Transcribed Image Text:**Match the formula of the exponential function to its graph.** ### Graphs of Exponential Functions Below are graphs of four different exponential functions. Your task is to match each graph to the correct formula from the list provided. 1. **Graph 1:** - **Description:** This graph shows a curve that starts from the top left quadrant, gradually decreases as it moves to the right, and approaches the x-axis without touching it. - **Graph Position:** First graph from the top. 2. **Graph 2:** - **Description:** This graph shows a curve that starts low at the left side, gradually increases, and steeply rises as it moves towards the right. - **Graph Position:** Second graph from the top. 3. **Graph 3:** - **Description:** This graph is the reflection of the first graph across the x-axis, decreasing exponentially into the negative y-values as it moves to the right. - **Graph Position:** Third graph from the top. 4. **Graph 4:** - **Description:** This graph is similar to the second graph but it stays in the negative y-values and decreases exponentially as it moves to the left. - **Graph Position:** Fourth graph from the top. ### Formulas for the Graphs a. \( f(x) = \left( \frac{1}{2} \right)^x \) b. \( f(x) = -\left( \frac{1}{2} \right)^x \) c. \( f(x) = 2^x \) d. \( f(x) = -(2^x) \) ### Matching Match each graph with the corresponding formula: 1. **Graph 1**: \( f(x) = \left( \frac{1}{2} \right)^x \) 2. **Graph 2**: \( f(x) = 2^x \) 3. **Graph 3**: \( f(x) = -\left( \frac{1}{2} \right)^x \) 4. **Graph 4**: \( f(x) = -(2^x) \) **Explanation for Appropriate Matching:** - **Graph 1** (a): Exponential decay, \( \left( \frac{1}{2} \right)^x \) shows the function decreasing as x increases, approaching zero. - **Graph
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