A polynomial written as a product shows its zeros: each factor is zero at one input. Adding a constant outside the function is a vertical shift; it changes the outputs but not the inputs. Find the zeros first, then use a Desmos list to evaluate the shifted function at every table input. Don’t stop at the unshifted outputs.
Hints
- Hint 1
A zero is an input that makes a function’s output . In a product, one factor equal to makes the whole product . Which factor vanishes at each input shown in the tables?
- Hint 2
The is outside , so it changes each output, not each input. Once you know what is at a listed input, what does adding make the new output?
Step-by-step
Use the factors, then evaluate the shift
Step 1Find the outputs before the shift
The listed inputs each make one factor of zero: , , and . If any factor is , the whole product is . So all three inputs give .
- Step 2
Define the shifted function
In , the changes each output, while the input stays the same. Type in Desmos, then name the requested rule . Desmos stores both rules so you can check the table inputs together.
- Step 3
Match the outputs to the table
Type . Desmos shows , in the same order as the inputs. So the table for has output at , , and . Choice B.
Lessons that teach this
- SAT Nonlinear FunctionsAdvancedCoreTransform nonlinear functions
- SAT Advanced AlgebraAdvancedCoreUse polynomial identities, factors, and unknown coefficients
- SAT Nonlinear FunctionsIntermediateEvaluate nonlinear functions and recover inputs
- DesmosIntermediateCoreTables, lists, and calculated columns
- DesmosAdvancedFactor, root, and remainder tests