Question

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) =

Answer 1

The graph g(x) represents the function f(x) = 3x + 1 translated units. To find the translation, determine the new y-intercept and the new slope of the line. The equation of the translated line is f(x) - 5 = 3x + 1, solving which gives us g(x) = 3x + 6.

Step-by-step explanation:

The graph g(x) represents the function f(x) = 3x + 1 translated units. To find the translation, we need to determine the new y-intercept and the new slope of the line.

The original line intersects the y-axis at -5, which means the y-intercept is -5. The new line intersects the y-axis at a different value, let's say y-intercept = k. The translation of the line is given by the equation f(x) + k. Since the y-intercept is -5, the equation of the translated line is f(x) - 5.

Next, we need to find the new slope of the line. The original slope is 3, which means there is a rise of 3 on the vertical axis for every increase of 1 on the horizontal axis. The slope remains the same for the translated line, so the equation of the translated line is f(x) - 5 = 3x + 1.

Solving the equation f(x) - 5 = 3x + 1 for g(x) gives us g(x) = 3x + 6.

Answer 2

translated 2

units up

g(x)= f(x-2)

Step-by-step explanation: