Both photos are needed to solve the problem. Thanks! ### Match the Graphs with Their Parametric EquationsThe diagram consists of six distinct graphs, each representing a different parametric equation. Below is a detailed description of each graph:#### Graph I- **Description:** The graph shows a curve starting from the bottom left, rising smoothly and steeply as it moves up and right. The curve resembles an elongated 'S' shape lying on its side.- **Axes:** The x-axis ranges from -1.0 to 1.0, and the y-axis from 0 to 2.#### Graph II- **Description:** This graph has a symmetrical shape across both axes, forming a bow-like or butterfly shape. The curves meet at the origin and extend towards the corners, pinching inward at both horizontal and vertical extremities.- **Axes:** The x-axis and y-axis both range from -1.0 to 1.0.#### Graph III- **Description:** The graph depicts a spiral centered at the origin. The spiral is tightly wound near the center and gradually expands as it moves outward.- **Axes:** The x-axis and y-axis both range from -0.2 to 0.2.#### Graph IV- **Description:** This graph shows two symmetric, looping curves resembling a double teardrop shape. The curves narrow at the bottom and widen at the top.- **Axes:** The x-axis ranges from -4 to 4, and the y-axis from 0 to 8.#### Graph V- **Description:** The graph displays a parabolic curve, opening upwards. The curve is smooth and broad, starting near the y-axis and moving outward as it rises.- **Axes:** The x-axis ranges from 0.5 to 3.0, and the y-axis from 0.0 to 1.0.#### Graph VI- **Description:** This graph illustrates a series of oscillating curves passing through the origin, forming an intricate pattern of loops both above and below the x-axis.- **Axes:** The x-axis and y-axis both range from -1.0 to 1.0. Each graph showcases unique mathematical properties and should be matched with their corresponding parametric equations to understand their behavior and underlying relationships fully. The image contains a multiple-choice question format with six parts labeled (a) through (f). Each part presents a pair of parametric equations for $x$ and $y$ in terms of the parameter $t$. Below each pair, there is a dropdown selection prompt labeled "---Select---".Here are the equations for each part:(a)\[ x = t^4 - t + 1, \quad y = t^2 \](b)\[ x = t^2 - 2t, \quad y = \sqrt{t} \](c)\[ x = \sin(2t), \quad y = \sin(t + \sin(2t)) \](d)\[ x = \cos(5t), \quad y = \sin(2t) \](e)\[ x = t + \sin(4t), \quad y = t^2 + \cos(3t) \](f)\[ x = \frac{\sin(2t)}{4 + t^2}, \quad y = \frac{\cos(2t)}{4 + t^2} \]There are no graphs or diagrams in the image.

Match the graph with their parametric equations.

(a) x = t* - t + 1, y = t2 Select--- v (b) x = 2 - 2t, y = VE --Select--- v (c) x = sin(2t), y = sin(t + sin(2t)) --Select- v (d) x = cos(5t), y = sin(2t) ---Select--- ♥ (e) x = t + sin(4t), y = t² + cos(3t) --Select--- V sin(2t) 4 + t2 ' cos(2t) y = 4 + t2 (f) x = ---Select-- v

(a) x = t* - t + 1, y = t2 Select--- v (b) x = 2 - 2t, y = VE --Select--- v (c) x = sin(2t), y = sin(t + sin(2t)) --Select- v (d) x = cos(5t), y = sin(2t) ---Select--- ♥ (e) x = t + sin(4t), y = t² + cos(3t) --Select--- V sin(2t) 4 + t2 ' cos(2t) y = 4 + t2 (f) x = ---Select-- v

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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Question

Both photos are needed to solve the problem. Thanks!

### Match the Graphs with Their Parametric Equations

The diagram consists of six distinct graphs, each representing a different parametric equation. Below is a detailed description of each graph:

#### Graph I
- **Description:** The graph shows a curve starting from the bottom left, rising smoothly and steeply as it moves up and right. The curve resembles an elongated 'S' shape lying on its side.
- **Axes:** The x-axis ranges from -1.0 to 1.0, and the y-axis from 0 to 2.

#### Graph II
- **Description:** This graph has a symmetrical shape across both axes, forming a bow-like or butterfly shape. The curves meet at the origin and extend towards the corners, pinching inward at both horizontal and vertical extremities.
- **Axes:** The x-axis and y-axis both range from -1.0 to 1.0.

#### Graph III
- **Description:** The graph depicts a spiral centered at the origin. The spiral is tightly wound near the center and gradually expands as it moves outward.
- **Axes:** The x-axis and y-axis both range from -0.2 to 0.2.

#### Graph IV
- **Description:** This graph shows two symmetric, looping curves resembling a double teardrop shape. The curves narrow at the bottom and widen at the top.
- **Axes:** The x-axis ranges from -4 to 4, and the y-axis from 0 to 8.

#### Graph V
- **Description:** The graph displays a parabolic curve, opening upwards. The curve is smooth and broad, starting near the y-axis and moving outward as it rises.
- **Axes:** The x-axis ranges from 0.5 to 3.0, and the y-axis from 0.0 to 1.0.

#### Graph VI
- **Description:** This graph illustrates a series of oscillating curves passing through the origin, forming an intricate pattern of loops both above and below the x-axis.
- **Axes:** The x-axis and y-axis both range from -1.0 to 1.0.

Each graph showcases unique mathematical properties and should be matched with their corresponding parametric equations to understand their behavior and underlying relationships fully.

The image contains a multiple-choice question format with six parts labeled (a) through (f). Each part presents a pair of parametric equations for $x$ and $y$ in terms of the parameter $t$. Below each pair, there is a dropdown selection prompt labeled "---Select---".

Here are the equations for each part:

(a)
\[ x = t^4 - t + 1, \quad y = t^2 \]

(b)
\[ x = t^2 - 2t, \quad y = \sqrt{t} \]

(c)
\[ x = \sin(2t), \quad y = \sin(t + \sin(2t)) \]

(d)
\[ x = \cos(5t), \quad y = \sin(2t) \]

(e)
\[ x = t + \sin(4t), \quad y = t^2 + \cos(3t) \]

(f)
\[ x = \frac{\sin(2t)}{4 + t^2}, \quad y = \frac{\cos(2t)}{4 + t^2} \]

There are no graphs or diagrams in the image.

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