A known input in function notation means you evaluate the rule: replace with the whole number inside the parentheses. Define the function in Desmos, then enter its name with that input. If the rule contains absolute value, subtract inside the bars first; taking the absolute value gives a nonnegative distance, even when the number inside is negative.
Hints
- Hint 1
In function notation, the number in is the input. Replace with in the rule, keeping the subtraction and the bars. What number ends up inside the bars?
- Hint 2
Absolute value is distance from . A negative number and its positive opposite have the same distance, so what happens to the negative sign before you add ?
Step-by-step
Define and evaluate the function
Step 1Enter the function rule
In function notation, means is the input. Type on the first Desmos line, keeping the bars around . Desmos now has the rule ready to evaluate.
- Step 2
Work out what the bars contain
Replace with the entire negative input:
Subtract inside the bars:
- Step 3
Apply absolute value
Absolute value means distance from , so a negative number inside the bars gives a positive distance:
- Step 4
Read the output
Type on the next Desmos line. It prints , the result of adding . So the value of is . Choice D.