For the function defined above, what is the value of ?

Solution available with step-by-step explanation

SAT Nonlinear Functions Question 202 | Free SAT Prep | Aniko

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Question 202·Easy·Nonlinear Functions

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$f(x)=4\left(\frac{1}{2}\right)^{x-1}$

For the function $f$ defined above, what is the value of $f(3)$ ?

For questions asking for a specific function value, immediately substitute the given x-value into the function, simplify step by step (especially exponents), and then compute carefully using order of operations. With exponential expressions, pay close attention to parentheses and the entire exponent (like $x-1$ ) before applying the base, then multiply any coefficients at the end.

Hints

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Start by substituting

Replace $x$ with 3 in the formula $f(x)=4\left(\frac{1}{2}\right)^{x-1}$ to write an expression for $f(3)$ .

Handle the exponent first

After substituting, simplify $3-1$ in the exponent before doing any multiplication.

Evaluate the power of 1/2

Carefully compute $\left(\frac{1}{2}\right)^2$ , then multiply that result by 4.

Desmos Guide

Enter the function

In Desmos, type f(x) = 4*(1/2)^(x-1) so the function is defined.

Evaluate f(3) directly

In a new line, type f(3) (or 4*(1/2)^(3-1)) and look at the numeric output that Desmos gives; that value is $f(3)$ .

Step-by-step Explanation

Substitute x = 3 into the function

The function is

f(x) = 4\left(\frac{1}{2}\right)^{x-1}.

To find $f(3)$ , replace $x$ with $3$ :

f(3) = 4\left(\frac{1}{2}\right)^{3-1}.

Simplify the exponent

Now simplify the exponent $3-1$ :

3 - 1 = 2.

So the expression becomes

f(3) = 4\left(\frac{1}{2}\right)^{2}.

Evaluate the power and multiply

Compute $\left(\frac{1}{2}\right)^2$ :

\left(\frac{1}{2}\right)^2 = \frac{1}{4}.

Now multiply by 4:

f(3) = 4 \cdot \frac{1}{4} = 1.

So the value of $f(3)$ is $1$ , which corresponds to choice B.

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