Graph g(x) is the graph of f(x) translated 6 units downwards and g(x) = 3x - 5
Transformations of a function,
- If a function 'f' is shifted by 'h' units left and 'k' units down, image function g(x) will be given by,
g(x) = f(x + h) - k
Given function in the question is → f(x) = 3x + 1
From the graph attached,
Let the equation of the line is,
y = mx + b
Here, m = Slope of the line
b = y-intercept
Since, slope of the line passing through two points [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] is given by,
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
Therefore, slope of the line passing through (0, -5) and (3, 4) will be,
[tex]m=\frac{4+5}{3-0}[/tex]
[tex]m=3[/tex]
[tex]\text{y-intercept} = b=-5[/tex]
Equation of the line will be,
[tex]y=3x-5[/tex]
And the function will be,
g(x) = 3x - 5
By comparing both the functions,
g(x) = f(x) - 6
Therefore, graph g(x) is the graph of f(x) translated 6 units downwards and g(x) = 3x - 5
Learn more about the transformations here,
https://brainly.com/question/26238840?referrer=searchResults
