Final answer:
The transformation is a vertical translation or shift. The graph of f(x)=6x-2 shifts up by 10 units to become the graph of g(x)=6x+8. Label and scale the graph to represent the transformation accurately.
Step-by-step explanation:
The kind of transformation that converts the graph of f(x) = 6x – 2 into the graph of g(x) = 6x + 8 is known as a vertical translation or vertical shift. In this case, the function f(x) is being shifted up by 10 units. To illustrate this, consider the graph of f(x), which we know is a straight line with a slope of 6 and a y-intercept of –2. If we add 10 to every y-value on the graph of f(x), we move each point up 10 units along the y-axis, resulting in the graph of g(x) with a y-intercept of +8.
To graph these functions, you would label the graph with f(x) and x. You would scale the x and y axes, ensuring the maximum x-value is at least 20 and the f(x) values accommodate up to 10, giving room to show the vertical shift. Beyond illustrating the transformation of f(x) to g(x), for a function such as f(x) = 20, you would draw a horizontal line at y = 20 for the domain 0 ≤ x ≤ 20, as f(x) is a constant function in this range.
To see this, let's compare the two equations. In the equation f(x) = 6x - 2, the constant term (-2) represents the y-intercept of the graph. On the other hand, in the equation g(x) = 6x + 8, the constant term (+8) represents the y-intercept of the graph. The change in the constant term from -2 to +8 leads to a vertical shift upward of 10 units.
Therefore, the kind of transformation that converts the graph of f(x) = 6x - 2 into the graph of g(x) = 6x + 8 is a vertical shift of 10 units upward.