At Westonci.ca, we connect you with the answers you need, thanks to our active and informed community. Experience the convenience of finding accurate answers to your questions from knowledgeable professionals on our platform. Connect with a community of professionals ready to provide precise solutions to your questions quickly and accurately.
Sagot :
To determine the equation of the new function after horizontally shifting the square root function [tex]$F(x) = \sqrt{x}$[/tex] to the right by eight units, we need to understand how horizontal shifts affect the equation of a function.
1. Parent Function:
The original or parent function is [tex]$F(x) = \sqrt{x}$[/tex].
2. Horizontal Shift:
A horizontal shift involves moving the graph of the function left or right along the x-axis. If we want to shift the function to the right by a certain number of units, we need to replace [tex]$x$[/tex] with [tex]$(x - h)$[/tex], where [tex]$h$[/tex] is the number of units we want to shift.
3. Shift Right by 8 Units:
If we want to shift the graph to the right by 8 units, we need to replace [tex]$x$[/tex] with [tex]$(x - 8)$[/tex]. This means our new function will be [tex]$F(x - 8)$[/tex].
4. Substitute and Simplify:
Substituting [tex]$(x - 8)$[/tex] into the original function, we get:
[tex]\[ F(x - 8) = \sqrt{x - 8} \][/tex]
Thus, the equation of the new function after shifting the square root function [tex]$F(x) = \sqrt{x}$[/tex] to the right by eight units is:
[tex]\[ F(x) = \sqrt{x - 8} \][/tex]
This new expression, [tex]$F(x) = \sqrt{x - 8}$[/tex], represents the horizontally shifted square root function.
1. Parent Function:
The original or parent function is [tex]$F(x) = \sqrt{x}$[/tex].
2. Horizontal Shift:
A horizontal shift involves moving the graph of the function left or right along the x-axis. If we want to shift the function to the right by a certain number of units, we need to replace [tex]$x$[/tex] with [tex]$(x - h)$[/tex], where [tex]$h$[/tex] is the number of units we want to shift.
3. Shift Right by 8 Units:
If we want to shift the graph to the right by 8 units, we need to replace [tex]$x$[/tex] with [tex]$(x - 8)$[/tex]. This means our new function will be [tex]$F(x - 8)$[/tex].
4. Substitute and Simplify:
Substituting [tex]$(x - 8)$[/tex] into the original function, we get:
[tex]\[ F(x - 8) = \sqrt{x - 8} \][/tex]
Thus, the equation of the new function after shifting the square root function [tex]$F(x) = \sqrt{x}$[/tex] to the right by eight units is:
[tex]\[ F(x) = \sqrt{x - 8} \][/tex]
This new expression, [tex]$F(x) = \sqrt{x - 8}$[/tex], represents the horizontally shifted square root function.
We hope you found this helpful. Feel free to come back anytime for more accurate answers and updated information. Thank you for choosing our platform. We're dedicated to providing the best answers for all your questions. Visit us again. Westonci.ca is your trusted source for answers. Visit us again to find more information on diverse topics.