f :: Number -> Number Consumes a number, multiplies by 3 to produce the result g :: Number -> Number Consumes a number, adds six to produce the result h :: Number -> Number Consumes a number, subtracts one to produce the result fx = 3x$\displaystyle f(x) = 3x$ gx = x + 6$\displaystyle g(x) = x + 6$ hx = x - 1$\displaystyle h(x) = x - 1$

For each function composition diagrammed below, translate it into the equivalent Circle of Evaluation for Order of Operations. Then write expressions for both versions of the Circles of Evaluation, and evaluate them for x = 4$\displaystyle x = 4$. The first one has been completed for you.

Function Composition Order of Operations Translate & Evaluate

1

h
g
f
 x
(h (g (f x)))

​-
+
​*
 3 x
6
1
(​- (+ (​* 3 x) 6) 1)

 Composition: h​(​g​(​f​(​x​)​)​) Operations: (​(​3 * x​) + 6​) - 1 Evaluate for x = 4 h(g(f4)) = 17$\displaystyle h(g(f(4))) = 17$

2

g
f
h
 x
(g (f (h x)))

 Composition: Operations: Evaluate for x = 4

3

h
f
g
 x
(h (f (g x)))

 Composition: Operations: Evaluate for x = 4

4

f
h
g
 x
(f (h (g x)))

 Composition: Operations: Evaluate for x = 4

These materials were developed partly through support of the National Science Foundation, (awards 1042210, 1535276, 1648684, and 1738598). Bootstrap by the Bootstrap Community is licensed under a Creative Commons 4.0 Unported License. This license does not grant permission to run training or professional development. Offering training or professional development with materials substantially derived from Bootstrap must be approved in writing by a Bootstrap Director. Permissions beyond the scope of this license, such as to run training, may be available by contacting contact@BootstrapWorld.org.