Question

question 38 points 3

if \\(y\\) = \frac{3}{6}|x - 6| - 2 then it ______.

a curve

open upwards

Explanation:

Identify the function type and its standard form

The given equation is:

$$y = \frac{3}{6}|x - 6| - 2$$

This is an absolute value function of the form \(y = a|x - h| + k\), where \(a = \frac{3}{6} = \frac{1}{2}\), \(h = 6\), and \(k = -2\).

Analyze the shape of the graph

An absolute value function of the form \(y = a|x - h| + k\) consists of two linear rays meeting at a vertex, forming a "V" shape rather than a smooth curve. Thus, it is not "a curve".

Determine the direction of opening

The coefficient \(a = \frac{1}{2}\) is positive (\(a > 0\)). When the leading coefficient of an absolute value function is positive, the graph opens upwards.

Answer:

• a curve
• open upwards (Correct answer)