find the function that is finally graphed after the following transformations are applied to y=square root x in the order listed.
a. reflected about the x-axis
b. shift up 7 units
c. shift right 5 units
y=?
would the answer be:
y=sqrt(-x-5)-7
y = √x
reflect in x: (x,y) -> (x,-y)
y = -√x
shift up 7
y = -√x + 7
shift right 5
y = -√(x-5) + 7
To find the function after the given transformations are applied to y = sqrt(x), we need to apply each transformation one by one in the given order.
a. Reflection about the x-axis:
To reflect a function about the x-axis, we multiply the function by -1. This will flip the graph of the function upside down.
So, y = -sqrt(x) represents the reflection of y = sqrt(x) about the x-axis.
b. Shift up 7 units:
To shift a function up, we add a positive constant to the original function equation. In this case, we need to shift y = -sqrt(x) up by 7 units. So the new equation becomes:
y = -sqrt(x) + 7
c. Shift right 5 units:
To shift a function to the right, we subtract a positive constant from the input (x) in the function. In this case, we need to shift y = -sqrt(x) + 7 to the right by 5 units. So the new equation becomes:
y = -sqrt(x - 5) + 7
Therefore, the final function graphed after the given transformations are applied to y = sqrt(x) in the given order is:
y = -sqrt(x - 5) + 7