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

Solution available with step-by-step explanation

SAT Nonlinear Functions Question 22 | Free SAT Prep | Aniko

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Question 22·Easy·Nonlinear Functions

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The function $g$ is defined by

g(t)=3t^2-5.

What is the value of $g(t)$ when $t=2$ ?

For function-evaluation questions, immediately substitute the given input into the function, then simplify carefully using the order of operations: exponents first, then multiplication/division, and finally addition/subtraction. Write each small step (like computing the square and then the product) to reduce careless mistakes, especially with exponents and negative or constant terms.

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Use the function definition

You are given $g(t)=3t^2-5$ and asked for $g(2)$ . Start by substituting $t=2$ into the expression.

Remember order of operations

After substituting $2$ for $t$ , handle the exponent first: compute $2^2$ before multiplying by $3$ or subtracting $5$ .

Finish with subtraction

Once you have simplified $3t^2$ at $t=2$ , subtract $5$ from that result to get the final value.

Desmos Guide

Evaluate the expression in Desmos

In Desmos, type 3(2)^2-5 into an expression line (or first define g(t)=3t^2-5 and then type g(2)). The calculator will display a single numerical result—that number is the value of $g(2)$ .

Step-by-step Explanation

Substitute the given value into the function

The function is defined as $g(t)=3t^2-5$ . We are asked for $g(2)$ , so replace $t$ with $2$ :

g(2)=3\cdot 2^2-5

Apply exponents, then multiplication

Follow the order of operations (exponents before multiplication):

First, compute the exponent: $2^2=4$ .

Now multiply by 3: $3\cdot 4=12$ .

So now we have:

g(2)=12-5

Subtract to find the final value

Now subtract $5$ from $12$ :

12-5=7

So, the value of $g(t)$ when $t=2$ is $7$ .

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Desmos Guide

Step-by-step Explanation

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Step-by-step Explanation