The function is defined by . What is the value of ?

Solution available with step-by-step explanation

SAT Nonlinear Functions Question 67 | Free SAT Prep | Aniko

00:00

Question 67·Easy·Nonlinear Functions

0 / 234

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

For questions asking for a function value like $g(5)$ , immediately substitute the given number for $x$ , keep all parentheses, and then apply the order of operations: simplify inside parentheses, handle exponents, then do multiplication and addition. Writing each intermediate result (parentheses → square → multiply → add) helps avoid common errors like forgetting coefficients or misreading constants.

Hints

Click me!

Use the function definition

Start by writing $g(5)$ by replacing $x$ with 5 in the formula $g(x)=3(x-2)^2+1$ .

Follow the order of operations

After substituting, simplify inside the parentheses first, then apply the exponent, before doing any multiplication or addition.

Finish the arithmetic carefully

Once you have the value of $(5-2)^2$ , remember to multiply by 3 and then add 1 at the very end.

Desmos Guide

Enter the function

In Desmos, type g(x)=3(x-2)^2+1 on a line to define the function $g$ .

Evaluate the function at x = 5

On a new line, type g(5) and look at the numerical value Desmos returns; that value is $g(5)$ .

Step-by-step Explanation

Substitute the given x-value

The function is $g(x)=3(x-2)^2+1$ and we are asked for $g(5)$ .

Substitute $x=5$ into the function:

g(5)=3(5-2)^2+1

Simplify inside the parentheses, then square

First, simplify inside the parentheses:

5-2=3

Now square this result:

3^2=9

So the expression becomes:

g(5)=3\cdot 9+1

Multiply and then add to find the final value

Now multiply and then add:

Multiply: $3\cdot 9=27$
Add: $27+1=28$

So the value of $g(5)$ is 28.

Strategy

Hints

Desmos Guide

Step-by-step Explanation

Study Hints

Strategy

Hints

Desmos Guide

Step-by-step Explanation