Question 34·Easy·Nonlinear Functions
The function is defined by . What is the value of ?
For direct function-evaluation questions, immediately substitute the given input into the function, then carefully follow the order of operations: handle exponents first, then multiplication, then addition/subtraction. Write each intermediate step (like and ) to avoid mental-arithmetic slips, especially with negative signs, and only simplify to the final value at the end.
Hints
Interpret the function notation
means you should replace with 3 in the expression . Write out what the expression becomes when .
Follow the order of operations
After you substitute , handle the exponent on 3 first (the part), then multiply by 2, and only then do the subtraction from 9.
Be careful with signs and the constant term
Make sure you keep the 9 at the beginning of the expression and subtract the whole product from it, rather than adding or dropping any part.
Desmos Guide
Evaluate the function in Desmos
In the Desmos expression line, type 9 - 2(3)^2. Desmos will show a single numeric output; that number is the value of according to the function .
Step-by-step Explanation
Understand what means
The function is defined by .
The notation means: plug in everywhere you see in the formula.
So start by writing:
Apply the exponent and multiplication
Use the order of operations: exponents first, then multiplication, then subtraction.
- Compute the exponent: .
- Multiply by 2: .
So the expression becomes:
Subtract to find the final value
Now simplify the subtraction:
So the value of is .