Solving a Shifted Rule
Part of the Functions & Transformations section of Coddy's Algebra 2 journey. Lesson 6 of 55.
When a curve moves to the side, the answers of its equation move by the same amount. x^2 = 9 has the answers 3 and -3. Move the curve 2 to the right, and the equation becomes (x - 2)^2 = 9. Now the answers are 5 and -1. Each answer moved 2 to the right.
The algebra shows the same thing. Take the square root of both sides, with both signs: x - 2 = 3 or x - 2 = -3. Add 2 to each: x = 5 or x = -1.
Challenge
For f(x) = x^2, solve f(x - 3) = 16. Find both inputs. Then open the graph on the paper and compare them with 4 and -4.
Try it yourself
f(x - 3) = 16
Solve for x
All lessons in Functions & Transformations
4Combining Functions
Adding FunctionsSubtracting FunctionsMultiplying FunctionsAt a Single NumberRecap: Combining10Functions in Stories
Writing the RuleUsing the RuleWorking BackwardUndoing a ConversionRecap: Stories5Composition
One Inside AnotherOrder MattersA Function of ItselfComposing RulesBreaking ApartRecap: Composition8Stretching and Flipping
Taller and FlatterFlipping OverFlip, Then ShiftReading the RuleRecap: Stretch and Flip