Answer:
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)
- If f(x) translated k units up, then its image g(x) = f(x) + k
- If f(x) translated k units down, then its image g(x) = f(x) - k
The form of the linear function is f(x) = m x + b, where
- m is the slope of the line
- b is the y-intercept (value y at x = 0)
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
