What type of function is h? ### Exploring Function Composition: Cosine and Additional Functions**Graphed Function Explanation:**The function shown in the graph is the result of combining two functions, $ g(x) $ and $ h(x) $, through addition. The graph demonstrates how these two functions interact to form a single, more complex waveform.The function $ g $ is defined as a cosine function. This information allows us to infer certain characteristics about the graph, as cosine functions typically represent periodic waveforms.**Graph Analysis:**In the visual representation, the graph exhibits various features:- **X-Axis Range:** The graph spans values from approximately -5 to +5.- **Y-Axis Range:** Vertical values extend from roughly -100 to +100.- **Curvature Patterns:** There are periodic oscillations clearly indicative of the cosine function's influence.- **Additional Influence:** The overall shape also presents an underlying curved trend, suggesting another influencing function, $ h(x) $, superimposed on the cosine wave.**Question & Answer Section:****Question:**What type of function is $ h $? Explain why you chose your function.**Answer Choices:**1. $ h(x) $ is a **linear** function because the graph appears to be a straight line with a periodic cosine function making the wave.2. $ h(x) $ is a **quadratic** function because the graph appears to be a parabola with a periodic cosine function making the wave.3. $ h(x) $ is a **radical** function because the graph appears to be a curve with a periodic cosine function making the wave.4. $ h(x) $ is a **rational or reciprocal** function because the graph appears to be a hyperbola with a periodic cosine function making the wave.**Explanation Summary:**- **Linear Function:** A straight-line influence would not produce the significant curvature seen in the graph.- **Quadratic Function:** A parabolic influence is a strong candidate, as it can account for the overall curved shape.- **Radical Function:** A square root function introduces distinct curvature but would have asymmetry not observed here.- **Rational or Reciprocal Function:** The hyperbolic characteristic appears less likely, given the smooth nature of the overall shape.The most fitting choice appears to be the quadratic function. The graph's parabolic nature combined with the superimposed periodic cosine wave suggests \( h(x

Name: What type of function is h? ### Exploring Function Composition: Cosine
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Description: What type of function is h? ### Exploring Function Composition: Cosine and Additional Functions**Graphed Function Explanation:**The function shown in the graph is the result of combining two functions, $ g(x) $ and $ h(x) $, through addition. The

Graph of h(x)=f(x)+g(x) is given where f(x) is cosine function. To determine: The function g(x).

Answered: N -10+ -30+ (x)+(x)=x too-

Math

Advanced Math

N -10+ -30+ (x)+(x)=x too-

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

What type of function is h?

### Exploring Function Composition: Cosine and Additional Functions

**Graphed Function Explanation:**

The function shown in the graph is the result of combining two functions, $ g(x) $ and $ h(x) $, through addition. The graph demonstrates how these two functions interact to form a single, more complex waveform.

The function $ g $ is defined as a cosine function. This information allows us to infer certain characteristics about the graph, as cosine functions typically represent periodic waveforms.

**Graph Analysis:**

In the visual representation, the graph exhibits various features:
- **X-Axis Range:** The graph spans values from approximately -5 to +5.
- **Y-Axis Range:** Vertical values extend from roughly -100 to +100.
- **Curvature Patterns:** There are periodic oscillations clearly indicative of the cosine function's influence.
- **Additional Influence:** The overall shape also presents an underlying curved trend, suggesting another influencing function, $ h(x) $, superimposed on the cosine wave.

**Question & Answer Section:**

**Question:**
What type of function is $ h $? Explain why you chose your function.

**Answer Choices:**
1. $ h(x) $ is a **linear** function because the graph appears to be a straight line with a periodic cosine function making the wave.
2. $ h(x) $ is a **quadratic** function because the graph appears to be a parabola with a periodic cosine function making the wave.
3. $ h(x) $ is a **radical** function because the graph appears to be a curve with a periodic cosine function making the wave.
4. $ h(x) $ is a **rational or reciprocal** function because the graph appears to be a hyperbola with a periodic cosine function making the wave.

**Explanation Summary:**

- **Linear Function:** A straight-line influence would not produce the significant curvature seen in the graph.
- **Quadratic Function:** A parabolic influence is a strong candidate, as it can account for the overall curved shape.
- **Radical Function:** A square root function introduces distinct curvature but would have asymmetry not observed here.
- **Rational or Reciprocal Function:** The hyperbolic characteristic appears less likely, given the smooth nature of the overall shape.

The most fitting choice appears to be the quadratic function. The graph's parabolic nature combined with the superimposed periodic cosine wave suggests \( h(x

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