Which function is represented below?
Looking at our graph, we can see that it’s from the family of the square root graph, which looks something like this.
So what we have for this red graph is a transformation of the square root graph.
First looking at what the variable
a would do to the square root graph, well if a is less than zero, it will essentially make it go
upside down; it will reflect it over the 𝑥-axis. If the absolute value of a is greater than one, it
will make the graph stretch vertically, and if the absolute value is between zero and one, it
will compress it vertically.
Now there are two other transformations that could happen to this
graph represented by ℎ and 𝑘. ℎ will represent a horizontal shift and 𝑘 will represent a
vertical shift. Horizontal moves it left and right; vertical moves it up and down.
So looking at
the original 𝑦 equals the square root 𝑥 graph, it must have been flipped upside down. Since our
graph was indeed reflected over the 𝑥-axis, so it is upside down, a must be negative.
graph doesn’t seem to be stretched or compressed, so we can leave a as negative or negative one.
As for a horizontal shift, our graph did shift left three, so we need to put in negative three
for each. However, our graph was not shifted up or down, so we could put plus zero at the end.
we just need to simplify. This means 𝑔 of 𝑥, the function represented in the graph, is equal to
negative square root 𝑥 plus three.