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=___
5. write the function whose graph is the graph is the graph of y=(x+4)^2, but is reflected about the y- axis y=____
6. write the function whose graph is the graph of y=x^2 but horizontally strectched by a factor of 8. y=____
3. y=sqrt(x-3)
4. y=|x|-8
5. y=-(x+4)^2
6. y=x^2/8
To write the functions requested, we need to apply certain transformations to the original functions. Here's how you can determine the correct forms of the functions:
3. To shift the graph of the function y = √x to the left 3 units, we need to replace x with (x + 3) in the original function. Therefore, the correct function is y = √(x + 3).
4. To shift the graph of the function y = |x| down 8 units, we need to subtract 8 from the original function. Therefore, the correct function is y = |x| - 8.
5. To reflect the graph of the function y = (x + 4)^2 about the y-axis, we need to replace x with -x in the original function. Therefore, the correct function is y = (-x + 4)^2.
6. To horizontally stretch the graph of the function y = x^2 by a factor of 8, we need to divide x by 8 in the original function. Therefore, the correct function is y = (1/8)x^2.
Keep in mind that these transformations are applied to the original functions to achieve the desired results.
3. To shift the graph of y = √x to the left 3 units, we need to subtract 3 from the x-coordinate. Therefore, the function is y = √(x - 3).
4. To shift the graph of y = |x| down 8 units, we need to subtract 8 from the y-coordinate. Therefore, the function is y = |x| - 8.
5. To reflect the graph of y = (x + 4)^2 about the y-axis, we need to change the sign of x. Therefore, the function is y = (-x + 4)^2.
6. To horizontally stretch the graph of y = x^2 by a factor of 8, we need to multiply the x-coordinate by 1/8. Therefore, the function is y = (1/8)x^2.