The graph g(x) is the graph of f(x) translated 2 units, right and g(x) = f(x - 2).
In Mathematics and Geometry, the point-slope form of a straight line can be calculated by using the following mathematical equation (formula):
Where:
- x and y represent the data points.
- m represent the slope.
First of all, we would determine the slope of the line by using these points (2, 1) and (0, -5);
Slope (m) = (-5 - 1)/(0 - 2)
Slope (m) = 3
At data point (0, -5) and a slope of 3, a function for this line can be calculated by using the point-slope form as follows:
y + 5 = 3(x - 0)
y = 3x - 5
g(x) = 3x - 5
Since f(x) pass through the point (0, 1) and g(x) pass through point (2, 1), the translation is given by;
Translation (h) = 2 - 0
Translation (h) = 2 (2 units right).
Therefore, g(x) = f(x - 2)
Complete Question:
Consider the function f(x)=3x+1 and the graph of the function g(x) shown below.
The graph g(x) is the graph of f(x) translated ____ units, ____ and ___.