3. write the function whose graph is the graph of y=sqrt of x, but is shifted to the left 3 units y=____
4. write the function whose graph is the graph of y=|x|, but is shifted down 8 units y=___
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To write the functions that you mentioned, we need to start with the original functions and then apply the indicated shifts.
3. To shift the graph of y = √x three units to the left, we need to replace the variable x with (x + 3) in our function. So, the function will be y = √(x + 3).
4. To shift the graph of y = |x| down by eight units, we need to subtract 8 from the function. So, the function will be y = |x| - 8.
By applying these transformations, we have shifted the graphs of the original functions accordingly.
3. To shift the graph of y = √x to the left 3 units, we need to replace x with (x + 3) in the equation. Therefore, the function becomes:
y = √(x + 3)
So, y = √(x + 3) represents the function whose graph is the graph of y = √x, but shifted 3 units to the left.
4. To shift the graph of y = |x| down 8 units, we need to subtract 8 from the equation. Therefore, the function becomes:
y = |x| - 8
So, y = |x| - 8 represents the function whose graph is the graph of y = |x|, but shifted down 8 units.