Final: Where f Lives

Part of the Functions & Transformations section of Coddy's Algebra 2 journey. Lesson 54 of 55.

This problem asks for the domain of $f\left(x\right) = \sqrt{21-3x}$ . A square root refuses some inputs, so the board holds the condition the inside must meet. Solve it to describe every input f accepts.

Challenge

Find the domain of $f\left(x\right) = \sqrt{21-3x}$ . The board holds the condition its inside must meet: solve it.

Try it yourself

21-3x \ge 0

Get $x$ alone on one side

Test yourself

This lesson includes a short quiz. Start the lesson to answer it and track your progress.

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 Apart Recap: 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 VFinal: Where f LivesFinal: 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