### Matching Exponential Function Formulas with Their GraphsExponential functions are mathematical expressions involving exponents, which often describe growth or decay processes.Below are four graphs of exponential functions and four corresponding equations from which you have to match each graph with the correct equation.#### Graphs of Exponential Functions1. **Graph 1**: The graph shows a curve passing from the positive y-axis to approach the negative x-axis and negative y-axis. It passes through the points roughly (0, -1), and the curve is continuously decreasing. This indicates it may be related to a negative exponential function with a base greater than 1.2. **Graph 2**: The graph shows a curve starting from a high positive y-value steeply decreasing towards zero but never crossing the x-axis. It passes through the points roughly at (0, 1) and becomes closer to 0 for positive values of x. This indicates it may represent an exponential decay function with a base between 0 and 1.3. **Graph 3**: The graph shows a curve starting negative and approaching zero from below as it moves to the right, passing through the origin at point (0, -1) and becoming a flat line very close to zero without ever reaching it. This indicates a negative exponential function with a base between 0 and 1.4. **Graph 4**: This graph demonstrates a typical exponential growth curve. It starts from the origin, moves upwards sharply as x increases, typical of a function with a base greater than 1. It passes through the origin at the point (0,1) and increases rapidly.#### Formulas for the GraphsLet's match these graphs to their correct formulas:a. \( f(x) = -(3^x) \)b. \( f(x) = \left(\frac{1}{2}\right)^x \)c. \( f(x) = 3^x \)d. \( f(x) = -\left(\frac{1}{2}\right)^x \)### Matching:- **Graph 1** matches with \( a. \ f(x) = -3^x \).- **Graph 2** matches with \( b. \ f(x) = \left( \frac{1}{2} \right)^x \).- **Graph 3** matches with \( d. \ f(x) = - \left( \frac

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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 P -5+ 5+ 4 3 2 7 -5 -4 -3 -2 -1 -1 -2 -3- -4 -5+ 5 4 3 2 -5 -4 -3 -2 -1 + -1 -2 -3 -4 -5- 5+ 4 3 2 1 -5 -4 -3 -2 -1 -1 -2 -3 -4 -5+ 4 5 1 2 3 4 5 1 2 3 4 5 1 2 3 4 5 2 3 4 5 a Formulas for the Graphs a. f(x) = - (3*) 1 b. f(x) (²¹) ² 2 c. f(x) = 3² d. f(x) = = 1 (¹) * 2

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 P -5+ 5+ 4 3 2 7 -5 -4 -3 -2 -1 -1 -2 -3- -4 -5+ 5 4 3 2 -5 -4 -3 -2 -1 + -1 -2 -3 -4 -5- 5+ 4 3 2 1 -5 -4 -3 -2 -1 -1 -2 -3 -4 -5+ 4 5 1 2 3 4 5 1 2 3 4 5 1 2 3 4 5 2 3 4 5 a Formulas for the Graphs a. f(x) = - (3) 1 b. f(x) (²¹) ² 2 c. f(x) = 3² d. f(x) = = 1 (¹) 2

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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Question

### Matching Exponential Function Formulas with Their Graphs

Exponential functions are mathematical expressions involving exponents, which often describe growth or decay processes.

Below are four graphs of exponential functions and four corresponding equations from which you have to match each graph with the correct equation.

#### Graphs of Exponential Functions

1. **Graph 1**: The graph shows a curve passing from the positive y-axis to approach the negative x-axis and negative y-axis. It passes through the points roughly (0, -1), and the curve is continuously decreasing. This indicates it may be related to a negative exponential function with a base greater than 1.

2. **Graph 2**: The graph shows a curve starting from a high positive y-value steeply decreasing towards zero but never crossing the x-axis. It passes through the points roughly at (0, 1) and becomes closer to 0 for positive values of x. This indicates it may represent an exponential decay function with a base between 0 and 1.

3. **Graph 3**: The graph shows a curve starting negative and approaching zero from below as it moves to the right, passing through the origin at point (0, -1) and becoming a flat line very close to zero without ever reaching it. This indicates a negative exponential function with a base between 0 and 1.

4. **Graph 4**: This graph demonstrates a typical exponential growth curve. It starts from the origin, moves upwards sharply as x increases, typical of a function with a base greater than 1. It passes through the origin at the point (0,1) and increases rapidly.

#### Formulas for the Graphs

Let's match these graphs to their correct formulas:

a. \( f(x) = -(3^x) \)

b. \( f(x) = \left(\frac{1}{2}\right)^x \)

c. \( f(x) = 3^x \)

d. \( f(x) = -\left(\frac{1}{2}\right)^x \)

### Matching:

- **Graph 1** matches with \( a. \ f(x) = -3^x \).

- **Graph 2** matches with \( b. \ f(x) = \left( \frac{1}{2} \right)^x \).

- **Graph 3** matches with \( d. \ f(x) = - \left( \frac

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