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Math Lesson 16.4.6 - Evaluating Composite Functions from a Graph
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Welcome to our Math lesson on Evaluating Composite Functions from a Graph, this is the sixth lesson of our suite of math lessons covering the topic of Composite Functions, you can find links to the other lessons within this tutorial and access additional Math learning resources below this lesson.
Evaluating Composite Functions from a Graph
We can find the value of a composite function at a given point even when the individual functions f(x) and g(x) are not explicitly given but only shown on the graph. In this case, we can use the information provided in the graph as a shortcut for finding values of each function or the resulting composite functions without having the need to know the exact formulas of the given functions. When doing this, we must take into account the fact that if the ordered pair (x, y) is a point of the function f(x), then f(x) = y. Given this, we follow the procedure below to calculate f ◦ g(a) for x = a:
- We find g(a) first so that the y-coordinate of g(x) for x = a is identified.
- Then, we find f[g(a)], i.e. the y-value of f(x) that corresponds to g(a).
Let's explain this procedure more in detail through the following example.
Example 5
The figure below shows two functions, f(x) and g(x).
Find:
- g ◦ f(7)
- f ◦ g(4)
Solution 5
- First, we must identify f(7). Looking at the f(x) graph, it is clear that f(7) = 5.
Next, we have to find g[f(7)]. This means identifying g(5) from the graph. Thus, it is easy to see that for x = 5, g(x) = -1.5. Therefore, g(5) = -1.5, i.e. g ◦ f(7) = g(5) = -1.5. - First, we must identify g(4). Looking at the g(x) graph, it is clear that g(4) = -1.
Next, we have to find f[g(4)]. This means identifying f(-1) from the graph. Thus, it is easy to see that for x = -1, f(x) = 1. Therefore, f(-1) = 1, i.e. f ◦ g(4) = f(-1) = 1.
You have reached the end of Math lesson 16.4.6 Evaluating Composite Functions from a Graph. There are 9 lessons in this physics tutorial covering Composite Functions, you can access all the lessons from this tutorial below.
More Composite Functions Lessons and Learning Resources
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- Continuing learning functions - read our next math tutorial: Piecewise Functions
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