Final answer:
The input substitution that creates a graph of function f(x) = x passing through points (0, -2.5) and (2.5, 0) is f(x-2.5). This represents a translation of the graph left by 2.5 units, aligning with the given points.
Step-by-step explanation:
To find this, let's consider the transformation of the function f(x) = x. The graph of f(x) = x would normally pass through the origin (0, 0) and have a slope of 1.
But the graph we're given passes through (0, -2.5) instead, which suggests a downwards shift or a translation to the left has taken place.
Since the graph still has a slope of 1 but is shifted left 2.5 units, the input substitution that created the given graph is f(x-2.5). This translates the graph of f(x) = x left by 2.5 units, matching the two given points.
To verify this, we can plug in the x-values from the points into f(x-2.5) and see if we get the corresponding y-values. For the point (0, -2.5), substituting x = 0 gives us f(0-2.5) = f(-2.5), which simplifies to -2.5.
For the point (2.5, 0), substituting x = 2.5 gives us f(2.5-2.5) = f(0), which simplifies to 0.
Thus, the graph described is indeed that of the function f(x-2.5).
Complete question:
Which input was substituted into the function f(x) = x to create the given graph, the graph of f(x) = x passes through (0, -2.5) and (2.5, 0)?