Need to know how to show work for the problem attached ### Match the Function with the GraphBelow is a task to match the function with its corresponding graph based on the given options.#### Functions:A) \( g(x) = \frac{1}{3}(x - 4)^2 \)B) \( g(x) = \frac{1}{3}x^2 + 4 \)C) \( g(x) = \frac{1}{3}x^2 - 4 \)D) \( g(x) = (x + 4)^2 \)#### Graph Explanation:In the middle of the image is a coordinate plane with the x-axis and y-axis ranging from -10 to 10. There is one parabola graphed which opens upwards and has a vertex at the point (0, -4).#### Visual Analysis of the Graph:1. **Vertex Identification**: The vertex of the parabola appears to be on the y-axis at (0, -4).2. **Opening Direction**: The parabola opens upwards, indicating a positive leading coefficient.Given this information:- Option A \(\left( g(x) = \frac{1}{3}(x - 4)^2 \right)\) shifts the graph to the right.- Option B \(\left( g(x) = \frac{1}{3}x^2 + 4 \right)\) shifts the graph upwards.- Option D \(\left( g(x) = (x + 4)^2 \right)\) shifts the graph to the left.- Option C \(\left( g(x) = \frac{1}{3}x^2 - 4 \right)\) shifts the graph downwards by 4 units.Considering the graph provided, the correct function that matches the graph is:**C) \( g(x) = \frac{1}{3}x^2 - 4 \)**The graph shows a parabola opening upwards with a vertex at (0, -4), which corresponds to the function \( g(x) = \frac{1}{3}x^2 - 4 \).

Given: graph of the function is provided. To be find: the equation of the curve. Concept: the…

Answered: Match the function with the graph. A)…

Math

Algebra

Match the function with the graph. A) g(x) = (x-4)² -10 B) g(x) = x² + 4 10 x C) g(x)=x²-4 D) g(x) = (x + 4)²

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

Need to know how to show work for the problem attached

### Match the Function with the Graph

Below is a task to match the function with its corresponding graph based on the given options.

#### Functions:

A) \( g(x) = \frac{1}{3}(x - 4)^2 \)

B) \( g(x) = \frac{1}{3}x^2 + 4 \)

C) \( g(x) = \frac{1}{3}x^2 - 4 \)

D) \( g(x) = (x + 4)^2 \)

#### Graph Explanation:

In the middle of the image is a coordinate plane with the x-axis and y-axis ranging from -10 to 10. There is one parabola graphed which opens upwards and has a vertex at the point (0, -4).

#### Visual Analysis of the Graph:
1. **Vertex Identification**: The vertex of the parabola appears to be on the y-axis at (0, -4).
2. **Opening Direction**: The parabola opens upwards, indicating a positive leading coefficient.

Given this information:

- Option A \(\left( g(x) = \frac{1}{3}(x - 4)^2 \right)\) shifts the graph to the right.
- Option B \(\left( g(x) = \frac{1}{3}x^2 + 4 \right)\) shifts the graph upwards.
- Option D \(\left( g(x) = (x + 4)^2 \right)\) shifts the graph to the left.
- Option C \(\left( g(x) = \frac{1}{3}x^2 - 4 \right)\) shifts the graph downwards by 4 units.

Considering the graph provided, the correct function that matches the graph is:

**C) \( g(x) = \frac{1}{3}x^2 - 4 \)**

The graph shows a parabola opening upwards with a vertex at (0, -4), which corresponds to the function \( g(x) = \frac{1}{3}x^2 - 4 \).

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