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Select the correct answer from each drop-down menu.
Consider the function f(x) = 3x + 1 and the graph of the function g(x) shown below.

A coordinate plane linear graph function shows a line intersecting Y-axis at minus 5 and X-axis at 1.5.
The graph g(x) is the graph of f(x) translated
units
, and g(x) =
.

Select the correct answer from each dropdown menu Consider the function fx 3x 1 and the graph of the function gx shown below A coordinate plane linear graph fun class=
Select the correct answer from each dropdown menu Consider the function fx 3x 1 and the graph of the function gx shown below A coordinate plane linear graph fun class=
Select the correct answer from each dropdown menu Consider the function fx 3x 1 and the graph of the function gx shown below A coordinate plane linear graph fun class=

Respuesta :

facundo3141592

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).

How to relate the function g(x) to the function f(x)?

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:

https://brainly.com/question/24850937

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