A function evaluation gives you an input and asks for the rule’s output. Define the rule in Desmos, then enter its name with that input. For a negative input, use parentheses wherever you substitute: its square is positive, and multiplying it by a negative number also gives a positive result. Replace every variable with the whole input.
Hints
- Hint 1
To evaluate a function, replace every in its rule with the input. Here the input is negative, so put it in parentheses each time. What happens when you square it?
- Hint 2
A negative times a negative is positive. That matters for the term with as well as the squared term. Define in Desmos, then enter on the next line.
Step-by-step
Substitute, then evaluate in Desmos
Step 1Put the input into the rule
means put in for every in the function, a rule that gives an output for each input:
The parentheses keep the whole negative input inside the square.
- Step 2
Read the output
Type in Desmos, then type on the next line. Desmos shows . The sign-sensitive terms are both positive: and . So the output at is . Choice D.