The function p is defined by $p(x) = nx^3 + 11$, where n is a constant. In the $xy$-plane, the graph of $y = p(x)$ passes through the point (-3, 65). What is the value of $p(4)$?
[correct answer: -117]
priority level: the Path to 650+ or higher
We are currently calling this question the unknown value Q. As is often the case, we are not seeking to be creative here. So, one route to the correct answer is to begin by determining the unknown value of n.
Given the point (-3, 65), we can plug in -3 for x within the original function. The 65 we swap in for p(x), since p(x) is y. Doing so, we arrive at….
$65 = n(-3)^3 + 11$
Subtracting 11 from both sides, we come to….
$54 = n(-3)^3$
That expression can become 54 = $n(-27)$. And then, when we divide both sides by -27, we arrive at $n$ = -2.
Knowing that $n$ = -2, we can rewrite the original function as $p(x) = -2x^3 + 11$.
To finish things out and determine the value of $p(4)$, we execute the classic function move of inputting 4 in for $x$ within the function.
$-2(4)^3 + 11$
Firing what’s above in to a calculator, we come to the correct final answer of -117.
If your desmos fluency is quite high, and you arrived at the correct answer here via desmos, we’re here to validate the legitimacy of this route. That said, given what the test writers could do within this type of question, we would encourage you to be comfortable with the traditional mathematical route we’ve mapped out above.