The parent function f(x) has
a square root function with a domain of x greater than or equal to 0
and a range of y greater than or equal to 0
First, what do we know about f(x)?
Now look at the changes that g(x) introduces into the graph.
First, we look inside the square root function. Notice there is an addition of 1 to x.
If we are adding inside the square root, this shifts a graph to the left. If we are subtracting, the graph will shift to the right.
In this scenario, g(x) shifts the graph of f(x) to the left by 1
Next, take note that we have a coefficient attached to the squareroot that is negative. Because the coefficient is negative, the graph is reflected about the x-axis.
Finally, note that the subtraction of value 3 at the end of this equation will cause a vertical shift down by 3 units.
The summarized answer will be:
​
A horizontal shift to the left by 1 unit, a reflection about the x-axis, and a vertical shift down by 3 units.
