Flipping Over
Part of the Functions & Transformations section of Coddy's Algebra 2 journey. Lesson 40 of 58.
A minus sign in front of a function turns every output into its opposite. A point 3 above the x-axis goes to 3 below it, and a point below comes up. The graph flips over the x-axis, like a page turned upside down.
Watch it on a V, g(x) = |x|. On y = -g(x), the corner (0, 0) stays where it is, because -0 is 0. The point (2, 2) goes to (2, -2), and (-3, 3) goes to (-3, -3). The V now opens downward, and its corner is the highest point.
Only the sign changes, never the distance. A point one step from the corner is still 1 away from it vertically, just on the other side. The same is true for any function you flip this way.
Challenge
Draw the graph of y = -f(x) for f(x) = x^2. The faint curve is f itself. Place the vertex, then drag the second point.
Try it yourself
Draw the graph
Test yourselfThis lesson includes a short quiz. Start the lesson to answer it and track your progress.
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: Stories2Expressions as Inputs
A Letter as InputA Sum as InputShifting the InputSolving f(x) = kRecap: Inputs as Expressions5Composition
One Inside AnotherOrder MattersA Function of ItselfComposing RulesBreaking ApartRecap: Composition8Stretching and Flipping
Taller and FlatterFlipping OverFlip, Then ShiftReading the RuleRecap: Stretch and Flip