I think its graph B ### Graph Analysis on Exponential Functions**Question**: Which graph shows \( f(x) = -3^x - 3 \) and its translation \( g(x) = f(x) + 9 \)?**Graph A Analysis**:- **Red Curve**: This exponential graph appears to represent \( f(x) = -3^x - 3 \), which typically starts with lower negative values and curves steeply upward as \( x \) increases.- **Blue Curve**: This shows the translation \( g(x) = f(x) + 9 \). The upward shift is evident, placing the blue curve above the red by the amount of 9 units on the \( y \)-axis.**Graph B Analysis**:- **Red Curve**: This exponential graph is consistent with a shifted form because it appears higher on the \( y \)-axis at \( x = 0 \) compared to Graph A.- **Blue Curve**: It is below the red curve, contrasting the function in Graph A.**Conclusion**:Graph A correctly demonstrates the function \( f(x) = -3^x - 3 \) and its translated form \( g(x) = f(x) + 9 \) where the blue curve is translated vertically by 9 units upwards. ### Graph Descriptions for Educational Website#### Graph C:- **Description**: This graph features two curves, one in blue and one in red, plotted on a Cartesian coordinate system.- **Blue Curve**: The blue curve represents an exponential function that starts with values close to zero for negative x-values and increases sharply as x-values are positive, indicating rapid growth.- **Red Curve**: The red curve shows a different exponential function, with a similar trend of sharp increase in positive x-values. However, its growth rate is slightly less steep compared to the blue curve.- **Intersection**: There is no visible intersection point on this graph.- **Axes**: The x-axis represents the horizontal coordinate and the y-axis represents the vertical coordinate. Both axes are labeled with intervals of 5 units.#### Graph D:- **Description**: Similar to Graph C, this graph displays two curves, one in blue and one in red, plotted on a Cartesian coordinate system.- **Blue Curve**: The blue curve represents an exponential function that begins with values near zero for negative x-values, then experiences rapid increase for positive x-values.- **Red Curve**: The red curve, like in Graph C, represents another exponential function with significant growth in positive x-values but is steeper than the blue line.- **Intersection**: No visible intersection is present between the two curves.- **Axes**: Both the x-axis and y-axis have tick marks at intervals of 5 units for reference.Each graph illustrates the behavior of exponential functions with different growth rates, demonstrating how they respond to changes in input values. These comparative graphs help visualize the concept of exponential growth and the influence of different base values in exponential functions.

Given: f(x)=3x-3 and its translation g(x)=f(x)+9. To find: Which of the given graph shows graphs of given functions.The y-intercept of the graph of function f(x)=3x-3 is given by, f(0)=30-3⇒f(0)=1-3⇒f(0)=-2 Also, the translation of f(x) is given by, g(x)=f(x)+9⇒g(x)=3x-3+9⇒g(x)=3x+6 Therefore, the y-intercept of g(x) is given by, g(0)=30+6⇒g(0)=1+6⇒g(0)=7 Among all the given graphs the in graph C) one graph has y-intercept is -2 and another graph has y-intercept 7. Hence the option C) is correct. Answer: Option C)

Answered: Which graph shows f (x) = 3 - 3 and its…

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Which graph shows f (x) = 3 - 3 and its translation g(x) = f(x) +9? A B 10 -10 15- 10

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Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...

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Question

I think its graph B

### Graph Descriptions for Educational Website

#### Graph C:
- **Description**: This graph features two curves, one in blue and one in red, plotted on a Cartesian coordinate system.
- **Blue Curve**: The blue curve represents an exponential function that starts with values close to zero for negative x-values and increases sharply as x-values are positive, indicating rapid growth.
- **Red Curve**: The red curve shows a different exponential function, with a similar trend of sharp increase in positive x-values. However, its growth rate is slightly less steep compared to the blue curve.
- **Intersection**: There is no visible intersection point on this graph.
- **Axes**: The x-axis represents the horizontal coordinate and the y-axis represents the vertical coordinate. Both axes are labeled with intervals of 5 units.

#### Graph D:
- **Description**: Similar to Graph C, this graph displays two curves, one in blue and one in red, plotted on a Cartesian coordinate system.
- **Blue Curve**: The blue curve represents an exponential function that begins with values near zero for negative x-values, then experiences rapid increase for positive x-values.
- **Red Curve**: The red curve, like in Graph C, represents another exponential function with significant growth in positive x-values but is steeper than the blue line.
- **Intersection**: No visible intersection is present between the two curves.
- **Axes**: Both the x-axis and y-axis have tick marks at intervals of 5 units for reference.

Each graph illustrates the behavior of exponential functions with different growth rates, demonstrating how they respond to changes in input values. These comparative graphs help visualize the concept of exponential growth and the influence of different base values in exponential functions.

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