1 Select the correct answer from each drop-down menu.
Consider the function RX) = 3x + 1 and the graph of the function gx) shown below.
Y
A
6
+
2
-6
.
- 2
2
6
-27
-6

The graph of g(x) is the graph of f(x) translated 6 units down, and

g(x) = f(x) - 6

Step-by-step explanation:

Let us revise the vertical translated of a function f(x)

The form of the linear function is f(x) = m x + b, where

We will the rules above to solve the question

∵ f(x) = 3x + 1

→ Compare f(x) with the form of the function above

∴ m = 3 and b = 1

∴ The y-intercept is (0, 1)

∴ The graph of f(x) intersects the y-axis at point (0, 1)

From the graph

∵ The graph of g(x) intersects the y-axis at the point (0, -5)

→ That means the y-intercept of g(x) is down the y-intercept of f(x)

∵ The difference between the y-intercepts g(x) and f(x) = -5 - 1 = -6

∴ The graph of f(x) is moved down by 6 units

∴ The image of f(x) is g(x) = f(x) - 6

The graph of g(x) is the graph of f(x) translated 6 units down, and

g(x) = f(x) - 6

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