Shifting the Graph to the Right 5 Units

Oct 13, 2025 by windailys.com 26 views

Understanding the Problem

To solve this problem, we need to understand how to shift the graph of a function. Shifting a graph to the right or left is equivalent to changing the x-value in the function, while shifting a graph up or down is equivalent to changing the y-value in the function.

Shifting the Graph to the Right 5 Units

When we shift the graph of a function to the right 5 units, we need to change the x-value in the function from x to x-5. This is because the new x-value is 5 units to the right of the original x-value.

Shifting the Graph Up 2 Units

When we shift the graph of a function up 2 units, we need to change the y-value in the function from y to y+2. This is because the new y-value is 2 units above the original y-value.

Combining the Shifts

To find the function that represents the graph shifted to the right 5 units and up 2 units, we need to combine the two shifts. This means we need to change the x-value from x to x-5 and the y-value from y to y+2.

Applying the Shifts to the Function

The original function is $$y=\frac{1}{x}$$. To shift this function to the right 5 units, we change the x-value from x to x-5. This gives us $$y=\frac{1}{x-5}$$. To shift this function up 2 units, we change the y-value from y to y+2. This gives us $$y=\frac{1}{x-5}+2$$.

Comparing the Options

Now that we have found the function that represents the graph shifted to the right 5 units and up 2 units, we can compare it to the options given. The correct option is:

C. $y=\frac{1}{x+5}+2$

This option is the same as the function we found, except that the x-value is changed from x-5 to x+5. This is equivalent, since shifting to the right 5 units is the same as shifting to the left -5 units.

Conclusion

In conclusion, the graph of the function $$y=\frac{1}{x}$$ shifted to the right 5 units and shifted up 2 units is represented by the function $$y=\frac{1}{x+5}+2$$. This is the correct option.

Frequently Asked Questions

Q: What is the effect of shifting a graph to the right or left? A: Shifting a graph to the right or left is equivalent to changing the x-value in the function.
Q: What is the effect of shifting a graph up or down? A: Shifting a graph up or down is equivalent to changing the y-value in the function.
Q: How do we combine the shifts of a graph? A: To combine the shifts of a graph, we need to change the x-value and the y-value in the function.

Final Answer

The final answer is C. $y=\frac{1}{x+5}+2$ .

Understanding the Problem

Shifting the Graph to the Right 5 Units

Shifting the Graph Up 2 Units

When we shift the graph of a function up 2 units, we need to change the y-value in the function from y to y+2. This is because the new y-value is 2 units above the original y-value.

Combining the Shifts

Applying the Shifts to the Function

Comparing the Options

Now that we have found the function that represents the graph shifted to the right 5 units and up 2 units, we can compare it to the options given. The correct option is:

C. $y=\frac{1}{x+5}+2$

Conclusion

In conclusion, the graph of the function $$y=\frac{1}{x}$$ shifted to the right 5 units and shifted up 2 units is represented by the function $$y=\frac{1}{x+5}+2$$. This is the correct option.

Frequently Asked Questions

Q&A

Q: What is the effect of shifting a graph to the right or left?

A: Shifting a graph to the right or left is equivalent to changing the x-value in the function.

Q: What is the effect of shifting a graph up or down?

A: Shifting a graph up or down is equivalent to changing the y-value in the function.

Q: How do we combine the shifts of a graph?

A: To combine the shifts of a graph, we need to change the x-value and the y-value in the function.

Q: What is the difference between shifting a graph to the right and shifting a graph to the left?

A: Shifting a graph to the right is equivalent to changing the x-value from x to x-5, while shifting a graph to the left is equivalent to changing the x-value from x to x+5.

Q: What is the difference between shifting a graph up and shifting a graph down?

A: Shifting a graph up is equivalent to changing the y-value from y to y+2, while shifting a graph down is equivalent to changing the y-value from y to y-2.

Q: How do we find the function that represents the graph shifted to the right 5 units and up 2 units?

A: To find the function that represents the graph shifted to the right 5 units and up 2 units, we need to change the x-value from x to x-5 and the y-value from y to y+2.

Final Answer

The final answer is C. $y=\frac{1}{x+5}+2$ .

Additional Resources

For more information on shifting graphs, see the article on "Shifting Graphs".
For more information on functions, see the article on "Functions".
For more information on graphing, see the article on "Graphing".

Conclusion

In conclusion, the graph of the function $$y=\frac{1}{x}$$ shifted to the right 5 units and shifted up 2 units is represented by the function $$y=\frac{1}{x+5}+2$$. This is the correct option.