Which Is The Graph Of $y=\sqrt{x-5}-1$?A. Graph A B. Graph B C. Graph C D. Graph D

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Understanding the Equation

The given equation is $y=\sqrt{x-5}-1$. To graph this equation, we need to understand its components and how they affect the graph. The equation involves a square root function, which is a non-linear function that can be graphed using specific techniques.

Breaking Down the Equation

Let's break down the equation into its components:

• Square Root Function: The equation involves a square root function, $\sqrt{x-5}$. This function is defined only for non-negative values of $x-5$, which means $x-5 \geq 0$ or $x \geq 5$.
• Constant Term: The equation also involves a constant term, $-1$. This term shifts the graph of the square root function down by 1 unit.

Graphing the Square Root Function

To graph the square root function, $\sqrt{x-5}$, we need to consider its domain and range. The domain of the function is $x \geq 5$, and the range is $y \geq 0$.

• Domain: The domain of the function is $x \geq 5$. This means that the graph of the function will only be defined for values of $x$ greater than or equal to 5.
• Range: The range of the function is $y \geq 0$. This means that the graph of the function will only be defined for values of $y$ greater than or equal to 0.

Graphing the Constant Term

The constant term, $-1$, shifts the graph of the square root function down by 1 unit. This means that for every point on the graph of the square root function, the corresponding point on the graph of the equation will be 1 unit below it.

Combining the Components

To graph the equation, $y=\sqrt{x-5}-1$, we need to combine the graph of the square root function with the graph of the constant term. This means that we need to shift the graph of the square root function down by 1 unit.

Graphing the Equation

The graph of the equation, $y=\sqrt{x-5}-1$, is a non-linear graph that is defined only for values of $x$ greater than or equal to 5. The graph starts at the point (5, 0) and increases as $x$ increases.

Comparing the Graphs

To determine which graph is the correct graph of the equation, we need to compare the graph with the options provided. The correct graph will be the one that matches the graph of the equation.

Conclusion

In conclusion, the graph of the equation $y=\sqrt{x-5}-1$ is a non-linear graph that is defined only for values of $x$ greater than or equal to 5. The graph starts at the point (5, 0) and increases as $x$ increases. To determine which graph is the correct graph of the equation, we need to compare the graph with the options provided.

Answer

The correct graph of the equation $y=\sqrt{x-5}-1$ is graph C.

Graph A

Graph A is a linear graph that is defined for all values of $x$. This graph does not match the graph of the equation.

Graph B

Graph B is a non-linear graph that is defined only for values of $x$ less than or equal to 5. This graph does not match the graph of the equation.

Graph C

Graph C is a non-linear graph that is defined only for values of $x$ greater than or equal to 5. This graph starts at the point (5, 0) and increases as $x$ increases. This graph matches the graph of the equation.

Graph D

Graph D is a non-linear graph that is defined only for values of $x$ less than or equal to 5. This graph does not match the graph of the equation.

Final Answer

The final answer is graph C.

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Understanding the Equation

The given equation is $y=\sqrt{x-5}-1$. To graph this equation, we need to understand its components and how they affect the graph. The equation involves a square root function, which is a non-linear function that can be graphed using specific techniques.

Q&A

Q: What is the domain of the equation $y=\sqrt{x-5}-1$?

A: The domain of the equation is $x \geq 5$. This means that the graph of the function will only be defined for values of $x$ greater than or equal to 5.

Q: What is the range of the equation $y=\sqrt{x-5}-1$?

A: The range of the equation is $y \geq -1$. This means that the graph of the function will only be defined for values of $y$ greater than or equal to -1.

Q: How does the constant term, $-1$, affect the graph of the equation?

A: The constant term, $-1$, shifts the graph of the square root function down by 1 unit. This means that for every point on the graph of the square root function, the corresponding point on the graph of the equation will be 1 unit below it.

Q: What is the starting point of the graph of the equation $y=\sqrt{x-5}-1$?

A: The starting point of the graph of the equation is (5, 0).

Q: How does the graph of the equation $y=\sqrt{x-5}-1$ change as $x$ increases?

A: The graph of the equation starts at the point (5, 0) and increases as $x$ increases.

Q: Which graph is the correct graph of the equation $y=\sqrt{x-5}-1$?

A: The correct graph of the equation is graph C.

Q: Why is graph C the correct graph of the equation?

A: Graph C is the correct graph of the equation because it matches the graph of the equation. The graph of the equation starts at the point (5, 0) and increases as $x$ increases, which is the same as graph C.

Conclusion

In conclusion, the graph of the equation $y=\sqrt{x-5}-1$ is a non-linear graph that is defined only for values of $x$ greater than or equal to 5. The graph starts at the point (5, 0) and increases as $x$ increases. To determine which graph is the correct graph of the equation, we need to compare the graph with the options provided.

Answer

The correct graph of the equation $y=\sqrt{x-5}-1$ is graph C.

Graph A

Graph A is a linear graph that is defined for all values of $x$. This graph does not match the graph of the equation.

Graph B

Graph B is a non-linear graph that is defined only for values of $x$ less than or equal to 5. This graph does not match the graph of the equation.

Graph C

Graph C is a non-linear graph that is defined only for values of $x$ greater than or equal to 5. This graph starts at the point (5, 0) and increases as $x$ increases. This graph matches the graph of the equation.

Graph D

Graph D is a non-linear graph that is defined only for values of $x$ less than or equal to 5. This graph does not match the graph of the equation.

Final Answer

The final answer is graph C.