Question

question 1 of 8
use the drawing tools to form the correct answer on the graph.
the equations represent functions p and q:
p(x) = x - 2
q(x) = x + 2
the graph of (p · q)(x) is shown.
plot a point at the ordered pair that represents (p · q)(-4) on the graph of the combined function.

Explanation:

Step1: Recall the product of functions

The function \((p \cdot q)(x)\) is the product of \(p(x)\) and \(q(x)\), so \((p \cdot q)(x)=p(x)\cdot q(x)\).
Given \(p(x)=x - 2\) and \(q(x)=x + 2\), then \((p \cdot q)(x)=(x - 2)(x + 2)\). By the difference of squares formula \(a^2 - b^2=(a - b)(a + b)\), this simplifies to \((p \cdot q)(x)=x^2-4\).

Step2: Substitute \(x = - 4\)

To find \((p \cdot q)(-4)\), we substitute \(x=-4\) into the function \((p \cdot q)(x)=x^2 - 4\).
So \((p \cdot q)(-4)=(-4)^2-4\).
First, calculate \((-4)^2 = 16\), then \(16-4 = 12\).

Answer:

The ordered pair is \((-4,12)\), so we plot the point at \((-4,12)\) on the graph.