**Graphing Exponential Functions: Mastery Test**The following educational content is part of a mastery test on graphing exponential functions:### Graph Description- The image shows a Cartesian plane with a graph of an exponential function.- The y-axis ranges from -10 to 6, and the x-axis ranges from -10 to 10.- The exponential function depicted in the graph shows rapid growth starting from the left and moving upward as it progresses to the right.### QuestionWhat is the y-intercept of the function $g(x) = 2f(x) + 12$?### Answer OptionsA. $(0, 2)$ B. $(0, -1)$ C. $(0, 3)$ D. $(0, 1)$ **Note: The correct answer, according to the image, is indicated as option A: $(0, 2)$.**This content is intended for educational purposes to help users understand the concepts and calculations related to graphing exponential functions.### Understanding the Concepts- **Exponential Functions:** These are mathematical functions where the variable is in the exponent, commonly written as $f(x) = a \cdot b^x$.- **Y-Intercept:** This is the point where the graph of a function crosses the y-axis (i.e., where $x = 0$).### Steps to Determine the Y-Intercept:1. Substitute $x = 0$ in the function $g(x)$.2. Calculate the output value to find the corresponding y-intercept on the graph.

Answered: Image /qna-images/answer/6bf22a89-6c5f-46ea-9495-e9d9b4b8207b.jpg

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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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Correlation

Correlation defines a relationship between two independent variables. It tells the degree to which variables move in relation to each other. When two sets of data are related to each other, there is a correlation between them.

Linear Correlation

A correlation is used to determine the relationships between numerical and categorical variables. In other words, it is an indicator of how things are connected to one another. The correlation analysis is the study of how variables are related.

Regression Analysis

Regression analysis is a statistical method in which it estimates the relationship between a dependent variable and one or more independent variable. In simple terms dependent variable is called as outcome variable and independent variable is called as predictors. Regression analysis is one of the methods to find the trends in data. The independent variable used in Regression analysis is named Predictor variable. It offers data of an associated dependent variable regarding a particular outcome.

Question

**Graphing Exponential Functions: Mastery Test**

The following educational content is part of a mastery test on graphing exponential functions:

### Graph Description
- The image shows a Cartesian plane with a graph of an exponential function.
- The y-axis ranges from -10 to 6, and the x-axis ranges from -10 to 10.
- The exponential function depicted in the graph shows rapid growth starting from the left and moving upward as it progresses to the right.

### Question
What is the y-intercept of the function $g(x) = 2f(x) + 12$?

### Answer Options
A. $(0, 2)$
B. $(0, -1)$
C. $(0, 3)$
D. $(0, 1)$

**Note: The correct answer, according to the image, is indicated as option A: $(0, 2)$.**

This content is intended for educational purposes to help users understand the concepts and calculations related to graphing exponential functions.

### Understanding the Concepts
- **Exponential Functions:** These are mathematical functions where the variable is in the exponent, commonly written as $f(x) = a \cdot b^x$.
- **Y-Intercept:** This is the point where the graph of a function crosses the y-axis (i.e., where $x = 0$).

### Steps to Determine the Y-Intercept:
1. Substitute $x = 0$ in the function $g(x)$.
2. Calculate the output value to find the corresponding y-intercept on the graph.

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