Question

HELP its 400 points :(

List the transformations needed to graph this function, in the order that you would perform them.


y = -
`√(x) -3` + 2

Answer 1

Shift the graph of
`y = √(x)` 3 units to the right, 2 units up, and reflect across the x-axis

Explanation:

To find the different transformations, first separate the transformations into what effects the x and what effects the y.

Since the (x-3)^0.5 is inside the square root, the -3 affects the x-values of the function. Since the value is affecting the x-values of the function, its shift on the graph is opposite of what's in the equation. Although the equation shows -3, the graph is shifted opposite, so it's 3 units to the right (in the positive direction).

Since the - sign and the +2 is outside the square root, these values affect the y-values of the function and do exactly as you'd expect, not opposite of what's shown. Since +2 is shown in the equation, the graph shifts 2 units upwards. Finally, the - sign will reflect over the x-axis, since reflection across the x-axis will affect the y-values and not the x-values.