there are two correct options:
- A translation of 6 units down: g(x) = f(x) - 6
- A translation of 2 units to the right: g(x) = f(x - 2).
<h3>
How to relate the function g(x) to the function f(x)?</h3>
We know that:
f(x) = 3x + 1
Now, if we look at the graph of f(x), we can see that the y-intercept is at y = -5, and for each increase in one unit in the x-variable, there is an increase of 3 units in the y-variable.
Then the equation of g(x) is:
g(x) = 3*x - 5
Then g(x) is a translation downwards of 6 units, such that:
g(x) = f(x) - 6 = (3x + 1) - 6 = 3x - 5
And we also could write it as a horizontal translation of 2 units to the right:
g(x) = f(x - 2) = 3*(x - 2) + 1 = 3*x - 3*2 + 1 = 3x - 5
So there are two correct options:
- A translation of 6 units down: g(x) = f(x) - 6
- A translation of 2 units to the right: g(x) = f(x - 2).
If you want to learn more about translations:
brainly.com/question/24850937
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