Question

Select the correct answer from each drop-down menu.
Consider the function fx) = 3x + 1 and the graph of the function g(x) shown below.
6
4
2-
-6
2
x
-4
12
6
-2
-4
-6
The graph g) is the graph of Ax) translated
e units
®, and g(x) =
e
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Answer 1

9514 1404 393

Answer:

• 6 units
• down
• g(x) = 3x -5

Step-by-step explanation:

The y-intercept of f(x) = 3x+1 is +1.

The y-intercept of the line shown on the graph is -5. This means the line graphed has a y-intercept that is 1-(-5) = 6 units below that of f(x).

To make the line on the graph, f(x) is translated 6 units down.

The graph shown has a slope of 3, like f(x) does. Its equation in slope-intercept form is ...

  g(x) = 3x -5 . . . . . . . . . line with slope 3 and y-intercept -5

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Additional comment

The translation down 6 units is equivalent in this case to a translation right 2 units. You will notice that g(2) = 1, where f(0) = 1. We suspect your pull-down menus do not offer the option of "2 units right." It is always the case for linear functions that vertical translation and horizontal translation (by perhaps a different amount) can bring about the same change in the graph.