Question 814·Easy·Math

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The function $h$ is defined by $h(t)=9-2t^2$ . What is the value of $h(3)$ ?

A function value such as $h(3)$ gives you an input and asks for the output. Replace the variable with the number inside the parentheses, or define the rule in Desmos and enter the function call. With a squared term, square the input before multiplying; including the coefficient in the square changes the result.

Hints

Hint 1
The input is the number inside the function’s parentheses, so $h(3)$ asks you to replace $t$ with $3$ . Keep the subtraction and the coefficient exactly as written when you substitute.
Hint 2
In $-2t^2$ , the exponent applies to $t$ , not to the $2$ . Square $3$ first, then multiply that square by $2$ . Will you subtract more or less than $9$ ?

Step-by-step

Substitute, then evaluate in Desmos
Step 1
Put the input into the rule
The input in $h(3)$ is $3$ , so put $3$ wherever the rule uses $t$ :
$h(3)=9-2(3)^2.$
Only the $3$ is squared; the $2$ multiplies afterward.
Step 2
Enter the function rule
Type $h(t)=9-2t^2$ in Desmos. Keep the minus sign before $2$ : the rule subtracts the squared term. Desmos now has the function ready to evaluate.
Step 3
Read the output
On the next line, type $h(3)$ . Desmos shows $-9$ . That output checks out: square first, so $2(3^2)=18$ is subtracted from $9$ . The value of $h(3)$ is $-9$ . Choice B.

Question 814·Easy·Math

Strategy

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Step-by-step

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Strategy

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Step-by-step

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