Find the function that is finally graphed after following transformations are applied to the graph of y=�ãx in the order list
1. shift down 8 units
2. reflect the x-axis
3. reflect the y-axis
to shift f(x) down 8,
f(x)-8
to reflect in x-axis,
-(f(x)-8) = 8 - f(x)
to reflect in y-axis,
8 - f(-x)
To find the function that is finally graphed after applying the given transformations to the graph of y = x, we need to apply each transformation in the given order.
1. Shift down 8 units:
To shift a function down, we subtract the desired amount from the original function. So, for a shift down 8 units, we subtract 8 from the original function: y = x - 8.
2. Reflect the x-axis:
To reflect a function in the x-axis, we invert the sign of the y-coordinate. So, we multiply the whole function by -1: y = -(x - 8).
3. Reflect the y-axis:
To reflect a function in the y-axis, we invert the sign of the x-coordinate. So, we multiply the x-coordinate by -1: y = -(-x - 8).
Simplifying the expression, we get:
y = x + 8.
Therefore, the function that is finally graphed after applying the given transformations is y = x + 8.