Question 458·Easy·Math

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The function $g$ is defined by

g(x) = (x^2 - 4x + 7)\bigl(3 - \tfrac12 x\bigr)

What is the value of $g(2)$ ?

A function evaluation gives you an input and asks for the output. Replace every $x$ with that input, keeping the parentheses around each factor. In Desmos, define the function and then enter the requested value. Evaluate the factors before multiplying them. Watch the minus sign inside the second factor.

Hints

Hint 1
In function notation, the number inside the parentheses is the input. For $g(2)$ , every $x$ becomes $2$ . What does each of the two factors look like after that substitution?
Hint 2
The two parentheses are multiplied. In the second one, $\tfrac12 x$ means half of the input; subtract that amount from $3$ before multiplying the factors.

Step-by-step

Define and evaluate in Desmos
Step 1
Replace the input throughout the rule
$g(2)$ means put $2$ in for every $x$ , so
$g(2)=(2^2-4(2)+7)\left(3-\tfrac12(2)\right).$
Type $g(x)=(x^2-4x+7)(3-\tfrac12 x)$ in Desmos. Keep both parentheses: they are factors to multiply.
Step 2
Read the function's output
Type $g(2)$ on the next line. Desmos shows $6$ . The minus sign in $3-\tfrac12 x$ matters; changing it to a plus would give a different output. At input $2$ , the function's output is $6$ . Choice B.

Question 458·Easy·Math

Strategy

Hints

Step-by-step

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Strategy

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Step-by-step

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