Question 266·Easy·Math

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The function $g$ is defined by $g(x)=3\bigl(x-2\bigr)^2+1$ . What is the value of $g(5)$ ?

A function evaluation gives you an input and asks for the output. The number inside the function’s parentheses replaces $x$ in the rule. On the SAT, you can define the function in Desmos and then type the requested function call. Square the entire difference in parentheses before multiplying by the number outside.

Hints

Hint 1
In function notation, $g(5)$ means put $5$ in for $x$ ; it does not mean multiply $g$ by $5$ . What does the difference inside the rule’s parentheses become?
Hint 2
An exponent applies to the whole expression immediately before it. Keep $(5-2)$ together when you square it. Then multiply by the number outside the parentheses and add the constant last.

Step-by-step

Evaluate the function in Desmos
Step 1
Substitute the input
The $5$ in $g(5)$ is the input, so replace $x$ with $5$ : $g(5)=3(5-2)^2+1$ . Type $g(x)=3(x-2)^2+1$ in Desmos to define the rule. Keep the square on the entire difference $(5-2)$ , not on the $3$ .
Step 2
Read the output
Type $g(5)$ on the next line. Desmos shows $28$ : it squares $5-2$ before multiplying by $3$ and adding $1$ . So the value of $g(5)$ is $28$ . Choice B.

Question 266·Easy·Math

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