The function is defined by . What is the value of ?
For function-evaluation questions, immediately substitute the given input into every in the function, using parentheses to avoid sign mistakes. Simplify inside parentheses first, then multiply. If the function is a product of factors, quickly check whether any factor becomes after substitution—if so, you can skip the remaining multiplication and know the entire expression equals , saving time.
Hints
Focus on what the notation means
means you take the function rule and plug in everywhere you see .
Substitute carefully with parentheses
Rewrite the function as before simplifying. Do not skip writing the parentheses.
Think about multiplying by zero
After you simplify and , check whether any factor becomes . What happens to a product if one of its factors is ?
Desmos Guide
Enter the function
In Desmos, type h(x)=5(x+1)(x-4) on a new line so Desmos defines the function .
Evaluate the function at
On the next line, type h(-1) or, alternatively, add a table for and enter -1 in the -column. Look at the corresponding output; that -value is .
Step-by-step Explanation
Understand what means
The expression means "evaluate the function when ." So we replace every in the formula with .
Substitute into the function
Write
Now simplify inside the parentheses:
So we get
Use the zero-product idea to finish
Any product that includes a factor of is , no matter what the other factors are. Since has a factor, the value of is . The correct answer is C) .