Here's the graph of g(x) = 5/6 f(x), where the parent function is f(x) = x:
1. Transformation:
Since g(x) = 5/6 f(x), it is a vertical stretch of the parent function f(x) = x by a factor of 5/6. This means all points on the graph of f(x) will be vertically "pulled up" by a factor of 5/6.
2. Key points:
Origin (0, 0) remains the same for both functions.
Any point on the line y = x on the graph of f(x) will be stretched vertically by 5/6. For example, the point (1, 1) on f(x) becomes (1, 5/6) on g(x).
Similarly, the point (-2, -2) on f(x) becomes (-2, -5/3) on g(x).
3. Graphing:
Plot the original graph of f(x) = x (a diagonal line from the origin).
For each point on the line y = x, identify the corresponding point on the new graph by vertically moving it up by a factor of 5/6.
Connect these new points to create the graph of g(x) = 5/6 f(x).
The resulting graph of g(x) will be a steeper diagonal line than f(x), always lying above it because of the vertical stretch. It will pass through the same origin (0, 0) and maintain the same horizontal spacing between points, but all points will be 5/6 higher than their corresponding points on the graph of f(x).
The probable question can be: Draw the graph that shows the correct g(x) function, if the parent function is f(x)=x. g(x)=5/6 f(x)