Question

error analysis
describe and correct the error in graphing the function.
46.
the graph is incorrect its going upwards when it should be going down

Explanation:

Step1: Analyze the function \( y = -3|x| \)

The general form of an absolute - value function is \( y=a|x - h|+k \). For the function \( y=-3|x| \), where \( h = 0\), \( k = 0\) and \( a=-3 \). The value of \( a\) determines the direction the graph opens. If \( a>0 \), the graph of \( y = a|x| \) opens upwards, and if \( a < 0\), the graph opens downwards. Here, since \( a=-3<0 \), the graph of \( y=-3|x| \) should open downwards.

Step2: Describe the error

The given graph of \( y = - 3|x| \) is opening upwards, which is incorrect. The correct graph should open downwards because the coefficient of \( |x| \) is negative (\( a=-3<0 \)).

Step3: Correct the graph

To correct the graph, we need to reflect the incorrect (upward - opening) graph over the \( x\) - axis. So, for each point \((x,y)\) on the incorrect graph, the corresponding point on the correct graph should be \((x, - y)\). For example, if the incorrect graph has a point \((1,3)\) (since when \( x = 1\), \( y=-3|1|=-3\), but the incorrect graph shows positive \( y\) - value for positive \( x\)), the correct point should be \((1,-3)\). After reflecting all such points, the graph will open downwards, which is the correct graph for \( y=-3|x| \).

Answer:

The error is that the graph of \( y = - 3|x| \) is opening upwards, but it should open downwards (because \( a=-3<0\) for the absolute - value function \( y=a|x|\), and a negative \( a\) means the graph opens downwards). To correct it, reflect the given (upward - opening) graph over the \( x\) - axis so that it opens downwards.