A table of a linear function gives input-output pairs. A rule like changes each output, not its input. With equation choices, the quickest route may be to change one table output and test the choices at that input in Desmos. One matching point settles the question only if it leaves a single choice.
Hints
- Hint 1
An output is the value a function returns for an input. Pick the row whose output is . What happens to that output when you subtract ?
- Hint 2
Every proposed rule for must give the changed output at the same input. Evaluate the rules there in Desmos. If only one matches, you don't need to find the entire rule for .
Step-by-step
Approach 1: Test a shifted table value
Step 1Find one output of h
The row with gives . Subtract from the output, not the input. Put into the rule for and use the table's zero output:
- Step 2
Find the rule that gives that output
Type in Desmos, then type each choice's right-hand expression using . Desmos prints , , , and , in order. Only gives the required , so . One point works here because it leaves only one choice; if two matched, you'd check another row. Choice B.
Approach 2: Fit the line, then shift it
Step 1Find the rule for f
Enter the table's inputs in and outputs in , keeping each pair in one row. Then type : the regression finds the line through the data. Under PARAMETERS, Desmos shows and , so . That's , not yet .
- Step 2
Lower the intercept
In , the intercept is the output at . Subtracting from every output leaves the slope alone and lowers that intercept. Type ; Desmos prints . So . Choice B.