A given function rule and a specific input call for evaluating the rule: replace with the input, then follow the operations in order. You can define the function in Desmos and enter the requested input to check the output. Absolute value is distance from zero, so a negative input becomes positive inside the bars. Treating the bars like ordinary parentheses gives the wrong sign.
Hints
- Hint 1
In function notation, the number in is the input, not the output. Replace in the rule with , keeping the bars around it. What expression does that give you?
- Hint 2
Absolute value tells you how far a number is from on the number line. The distance from to is positive, so find what the bars give before multiplying by .
Step-by-step
Substitute, then evaluate in Desmos
Step 1Put the input into the rule
In function notation, means replace with in the given rule. Keep the bars around the input: .
- Step 2
Find the absolute value
Absolute value is distance from , so . Replace the expression inside the bars and the bars themselves with : . Multiplying by instead would ignore the bars.
- Step 3
Read the function's output
Type in Desmos, then type on a new line. Desmos prints after taking the absolute value, multiplying by , and adding . So the value of is . Grid in 11.