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

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SAT Nonlinear Functions Question 136 | Free SAT Prep | Aniko

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Question 136·Easy·Nonlinear Functions

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The function $g$ is defined by $g(x)=2^{x+3}$ . What is the value of $g(2)$ ?

For function-evaluation questions, plug the given input directly into the function wherever you see $x$ , simplify step by step (handling exponents and parentheses first), and then compute any basic powers or arithmetic. For exponential functions like $2^{x+3}$ , simplify the exponent (here $x+3$ ) before evaluating the power, and memorize small powers of 2 (such as $2^1$ through $2^6$ ) to save time and avoid calculator dependence.

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Use the function definition

You are given $g(x)=2^{x+3}$ . To find $g(2)$ , replace $x$ with 2 everywhere in the expression.

Simplify inside the exponent

After substituting $x=2$ , focus first on simplifying the exponent $2+3$ before dealing with the power of 2.

Recall powers of 2

Once you know the exponent, think about powers of 2: $2^1, 2^2, 2^3, 2^4, 2^5, 2^6$ , and so on. Pick the one that matches your exponent.

Desmos Guide

Evaluate the expression directly

In a Desmos expression line, type 2^(2+3) and look at the numeric output that Desmos shows; that value is $g(2)$ for this function.

Step-by-step Explanation

Substitute the given input into the function

We are given the function $g(x)=2^{x+3}$ and asked for $g(2)$ .

Substitute $x=2$ into the expression:

g(2)=2^{2+3}

Simplify the exponent first

Now simplify the exponent $2+3$ .

2+3=5

So the function value becomes:

g(2)=2^5

Evaluate the power of 2 and choose the matching option

Compute $2^5$ by multiplying 2 by itself 5 times:

$2^1=2$
$2^2=4$
$2^3=8$
$2^4=16$
$2^5=32$

So $g(2)=32$ , which corresponds to choice C.

Strategy

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Desmos Guide

Step-by-step Explanation

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Strategy

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Desmos Guide

Step-by-step Explanation