Common Core · High school
HSF-IF.C.7.B
High school — Graph square root, cube root and piecewise-defined functions, including step functions and absolute value functions.
The 3 skills that cover it
- Rational Exponents & Radical EquationsRead a fractional exponent as a root, move between radical and exponent form, simplify with the exponent rules, and solve equations with a variable under a root, checking for solutions the squaring step invents.Read the lesson →
- Transformations of Any FunctionMove past the parabola: stretch a graph horizontally with f(kx), reflect it in the y-axis, apply several transformations in the right order, track where a single point goes, and do it all to square roots, cube roots, reciprocals, cubics and exponentials.Read the lesson →
- Piecewise Functions & ModellingBuild the function a situation needs: evaluate and write piecewise and step functions, find the average rate of change on an interval, turn a box, a fence or a price into a polynomial model, choose the right family, and use direct, inverse and joint variation.Read the lesson →
What a student should be able to do
- Evaluate an expression with a rational exponent such as 82/3, and take an nth root.
- Convert between radical form and rational-exponent form, and simplify using the exponent rules.
- Solve a radical equation by isolating the root and raising both sides to a power.
- Check every candidate in the original equation and reject extraneous solutions; state the domain of a radical function.
- Describe the effect of f(kx) and f(-x), and combine horizontal and vertical transformations in the correct order.
- Find the image of a point on y = f(x) under y = a f(b(x - h)) + k.
- Write the equation of a transformed square root, cube root, reciprocal, cubic, absolute value or exponential parent.
- Classify a function as even, odd or neither, and state the domain and range of a transformed function.
- Evaluate a piecewise or step function and match a description to its rule.
- Find the average rate of change of a function over an interval from a rule, a table or a graph.
- Build a polynomial or rational model from a described situation and use it to answer a question.
- Choose the function family a situation calls for, interpret its parameters, and solve direct, inverse and joint variation problems.