Answer:
Explanation:
We have been given a graph for f(x) and a table for g(x) and we have to find the transformation to map f(x) to g(x)
Let's find the function values for f(x) and g(x) at specific (easily distinguishable) x values for both
x f(x) from graph g(x) from table
0 4 0
1 3 -1
2 4 0
The function values for f(x) for x = -1 and x = 3 are a bit difficult to read since they do not cross at a grid intersection
From the above table we see that for a specific x, g(x) value is 4 less than the f(x) value
Therefore the transformation is
g(x) = f(x) - 4
Therefore g(x) is shifted downward by 4 points
I have plotted both f(x) and g(x) using the transformation; You can see the points fit
Ignore this part if you wish
The equation for f(x) is
f(x) = (x - 1)² + 3 in vertex form
or
f(x) = x² − 2x + 4 in polynomial form
g(x) will then be
x² - 2x + 4 - 4 = x² -2x