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

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SAT Linear Functions Question 34 | Free SAT Prep | Aniko

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Question 34·Easy·Linear Functions

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The function $p$ is defined by $p(x)=\dfrac{5x}{2}+6$ . What is the value of $p(4)$ ?

For function-evaluation questions, immediately substitute the given input into the function rule, rewrite the expression clearly, and then simplify using the order of operations—multiply and divide before adding or subtracting. Work step by step (especially with fractions) to avoid small arithmetic errors, and only then match your result to the answer choices.

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Interpret the function notation

Ask yourself: What does $p(4)$ tell you to do with the formula $p(x)=\dfrac{5x}{2}+6$ ?

Substitute the input value

Replace $x$ with $4$ in the expression $\dfrac{5x}{2}+6$ . Write out the new expression before simplifying.

Use the order of operations

After substituting, do the multiplication and division in the fraction first, then add the 6 at the end.

Desmos Guide

Evaluate the function using Desmos

In one line, type p(x) = (5x)/2 + 6. On a new line, type p(4). Desmos will display a single number next to p(4), which is the value of the function at $x=4$ .

Step-by-step Explanation

Understand what $p(4)$ means

The notation $p(4)$ means "take the function rule for $p(x)$ and plug in $x=4$ ." So you replace every $x$ in $p(x)=\dfrac{5x}{2}+6$ with $4$ .

Substitute and simplify step by step

Substitute $x=4$ into the function:

p(4) = \frac{5\cdot 4}{2} + 6

Now simplify the fraction first:

Multiply: $5\cdot 4 = 20$
Divide: $\dfrac{20}{2} = 10$

So the expression becomes $10 + 6$ .

Finish the calculation

Add the remaining numbers:

10 + 6 = 16

So $p(4) = 16$ , which corresponds to choice C.

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Desmos Guide

Step-by-step Explanation

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Desmos Guide

Step-by-step Explanation