### Match the Exponential Function with its GraphBelow are four exponential functions and their corresponding graphs. Match each function with the correct graph.#### Graphs:**Graph I:**- The graph shows a decreasing curve that starts above the x-axis and moves downward to the right, approaching zero but never crossing the x-axis. The curve is in the second quadrant then crosses to the first quadrant.**Graph II:**- The graph depicts a decreasing curve that starts above the x-axis and moves downward as it travels right, approaching the x-axis but never crossing it. The curve starts high in the second quadrant and drastically drops.**Graph III:**- The graph illustrates an increasing curve that starts near zero (but never touches the x-axis) and moves upwards as it moves to the right. The curve resides in the first quadrant.**Graph IV:**- The graph shows a decreasing curve that starts high above the x-axis and moves downward as it travels right, approaching but not touching the x-axis. The graph starts high in the first quadrant and gradually decreases.#### Functions:(a) $ f(x) = -2^x $ ---Select graph--- [I, II, III, IV](b) $ f(x) = -2^{-x} $ ---Select graph--- [I, II, III, IV](c) $ f(x) = 2^x $ ---Select graph--- [I, II, III, IV](d) $ f(x) = 2^{-x} $ ---Select graph--- [I, II, III, IV]#### Graph Explanations:- **Graph I:** - Represents a decreasing function with negative exponent, flipped vertically. - **Graph II:** - Represents a decreasing function of the form $ 2^{-x} $.- **Graph III:** - Represents an increasing function of the form $ 2^x $.- **Graph IV:** - Represents a decreasing function with a positive exponent, flipped horizontally.Match each function (a, b, c, d) with the appropriate graph (I, II, III, IV) based on the behavior and shape of the curves.

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Answered: Match the exponential function with its…

Match the exponential function with its graph. I II 2- III IV 2- (a) f(x) = -2x ---Select-- + (b) f(x) = -2¬x ---Select--- (c) f(x) = 2x ---Select--- (d) f(x) = 2¬x ---Select---

Algebra and Trigonometry (6th Edition)

6th Edition

ISBN:9780134463216

Author:Robert F. Blitzer

Publisher:Robert F. Blitzer

ChapterP: Prerequisites: Fundamental Concepts Of Algebra

Section: Chapter Questions

Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...

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Question

### Match the Exponential Function with its Graph

Below are four exponential functions and their corresponding graphs. Match each function with the correct graph.

#### Graphs:
**Graph I:**
- The graph shows a decreasing curve that starts above the x-axis and moves downward to the right, approaching zero but never crossing the x-axis. The curve is in the second quadrant then crosses to the first quadrant.

**Graph II:**
- The graph depicts a decreasing curve that starts above the x-axis and moves downward as it travels right, approaching the x-axis but never crossing it. The curve starts high in the second quadrant and drastically drops.

**Graph III:**
- The graph illustrates an increasing curve that starts near zero (but never touches the x-axis) and moves upwards as it moves to the right. The curve resides in the first quadrant.

**Graph IV:**
- The graph shows a decreasing curve that starts high above the x-axis and moves downward as it travels right, approaching but not touching the x-axis. The graph starts high in the first quadrant and gradually decreases.

#### Functions:
(a) $ f(x) = -2^x $
    ---Select graph--- [I, II, III, IV]

(b) $ f(x) = -2^{-x} $
    ---Select graph--- [I, II, III, IV]

(c) $ f(x) = 2^x $
    ---Select graph--- [I, II, III, IV]

(d) $ f(x) = 2^{-x} $
    ---Select graph--- [I, II, III, IV]

#### Graph Explanations:
- **Graph I:**
- Represents a decreasing function with negative exponent, flipped vertically.

- **Graph II:**
- Represents a decreasing function of the form $ 2^{-x} $.

- **Graph III:**
- Represents an increasing function of the form $ 2^x $.

- **Graph IV:**
- Represents a decreasing function with a positive exponent, flipped horizontally.

Match each function (a, b, c, d) with the appropriate graph (I, II, III, IV) based on the behavior and shape of the curves.

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