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Recap: Composition

Part of the Functions & Transformations section of Coddy's Algebra 2 journey. Lesson 23 of 55.

Challenge

For $f\left(x\right) = {x}^{2}+1$ and $g\left(x\right) = x-3$ , find $f\left(g\left(x\right)\right)$ as one rule, multiplied out and collected.

Try it yourself

f\left(g\left(x\right)\right)

Expand: multiply everything out

Given $f\left(x\right) = x^{2}+1$ $g\left(x\right) = x-3$

All lessons in Functions & Transformations

1Rules That Draw

Meet f(x)Negative Inputs Shifting the Input Solving f(x) = k

4Combining Functions

Adding Functions Subtracting Functions Multiplying Functions At a Single Number Recap: Combining

7Shifting Graphs

Up and Down Left and Right The Sign Inside Both at Once Shifting a V Recap: Shifts

10Functions in Stories

Writing the Rule Using the Rule Working Backward Undoing a Conversion Recap: Stories

2Expressions as Inputs

A Sum as Input Solving a Shifted Rule Recap: Inputs as Expressions

5Composition

One Inside Another Order Matters A Function of Itself Composing Rules Breaking ApartRecap: Composition

8Stretching and Flipping

Taller and Flatter Flipping Over Flip, Then Shift Reading the Rule Recap: Stretch and Flip

11Final Challenges

Final: Inside and Out Final: The Inverse Final: Move the V Final: Where f Lives Final: The Rental

3Domain and Range

What the Domain Is No Dividing by Zero No Roots of Negatives The Range Recap: Domain

6Inverse Functions

Undoing a Function Swap and Solve Fractions in Inverses Checking an Inverse A Value of the Inverse Recap: Inverses

9Rate of Change

Average Rate of Change A Line Keeps Its Rate A Curve Changes Rate Velocity as a Rate Recap: Rate of Change