**Title: Matching Graphs to Functions****Instructions:**Match each graph to one of the following functions. Select the function for each graph from the given options:- $ f(x) = x^2 + 2x + 3 $- $ f(x) = x^2 - 2x + 3 $- $ f(x) = x^2 - 2x $- $ f(x) = x^2 + 2x + 1 $- $ f(x) = x^2 - 1 $- $ f(x) = -x^2 - 1 $- $ f(x) = x^2 - 2x + 1 $- $ f(x) = x^2 + 2x $**Task:**Drag each function given above into the area below the appropriate graph, depending on which function is represented by which graph.**Graphs:**1. **Graph 13:** Features a downward opening parabola, centered around the y-axis. 2. **Graph 14:** Shows a parabola with a vertex at the origin, opening downwards.3. **Graph 15:** Displays a standard parabola opening upwards.4. **Graph 16:** Depicts a parabola opening upwards with a vertex away from the origin.5. **Graph 17:** Shows an upward opening parabola shifted slightly to the left.6. **Graph 18:** Features a parabola opening upwards, vertex closer to the y-axis.7. **Graph 19:** Displays a standard parabola with a vertex closer to the x-axis.8. **Graph 20:** Shows a parabola opening upwards, with fewer horizontal shifts.**Instructions for Users:**Review each graph and compare it to the functional behaviors given in the list. Drag the corresponding function to the space provided below each graph based on the shape and position of the parabola.**Note:**Ensure to verify the vertex form, axis of symmetry, and direction of the opening for accurate matching.

Given f(2) = x2 + 2x + 3 = x2 + 2x + 1 + 2 = (x + 1)2 + 2…

Match each graph to one of the following functions. Select the function for each graph from the given options. f(x) =x +2x+3 f(x) =Dx-2x+3 f(x)=x-2x f(x)=x +2x+1 f(x) =x-1 f(x)= -x-1 f(x)=x-2x+1 f(x) =x+2x Drag each function given above into the area below the appropriate graph, depending on which function is represented by which graph. 13. 14. 15. 16. -10 -10 (1.0) 10 -10-1,0 10 17 18. 19. 20. 10 -10 (-1,2 -1,-10 -10 10 -103 103

Match each graph to one of the following functions. Select the function for each graph from the given options. f(x) =x +2x+3 f(x) =Dx-2x+3 f(x)=x-2x f(x)=x +2x+1 f(x) =x-1 f(x)= -x-1 f(x)=x-2x+1 f(x) =x+2x Drag each function given above into the area below the appropriate graph, depending on which function is represented by which graph. 13. 14. 15. 16. -10 -10 (1.0) 10 -10-1,0 10 17 18. 19. 20. 10 -10 (-1,2 -1,-10 -10 10 -103 103

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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Concept explainers

Transformation of Graphs

The word ‘transformation’ means modification. Transformation of the graph of a function is a process by which we modify or change the original graph and make a new graph.

Exponential Functions

The exponential function is a type of mathematical function which is used in real-world contexts. It helps to find out the exponential decay model or exponential growth model, in mathematical models. In this topic, we will understand descriptive rules, concepts, structures, graphs, interpreter series, work formulas, and examples of functions involving exponents.

Question

**Title: Matching Graphs to Functions**

**Instructions:**

Match each graph to one of the following functions. Select the function for each graph from the given options:

- $ f(x) = x^2 + 2x + 3 $
- $ f(x) = x^2 - 2x + 3 $
- $ f(x) = x^2 - 2x $
- $ f(x) = x^2 + 2x + 1 $
- $ f(x) = x^2 - 1 $
- $ f(x) = -x^2 - 1 $
- $ f(x) = x^2 - 2x + 1 $
- $ f(x) = x^2 + 2x $

**Task:**

Drag each function given above into the area below the appropriate graph, depending on which function is represented by which graph.

**Graphs:**

1. **Graph 13:** Features a downward opening parabola, centered around the y-axis.
2. **Graph 14:** Shows a parabola with a vertex at the origin, opening downwards.
3. **Graph 15:** Displays a standard parabola opening upwards.
4. **Graph 16:** Depicts a parabola opening upwards with a vertex away from the origin.
5. **Graph 17:** Shows an upward opening parabola shifted slightly to the left.
6. **Graph 18:** Features a parabola opening upwards, vertex closer to the y-axis.
7. **Graph 19:** Displays a standard parabola with a vertex closer to the x-axis.
8. **Graph 20:** Shows a parabola opening upwards, with fewer horizontal shifts.

**Instructions for Users:**

Review each graph and compare it to the functional behaviors given in the list. Drag the corresponding function to the space provided below each graph based on the shape and position of the parabola.

**Note:**

Ensure to verify the vertex form, axis of symmetry, and direction of the opening for accurate matching.

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