which statement is true about $f(x)=-6|x + 5|-2$?\nthe graph of $f(x)$ is a horizontal compression of the…

which statement is true about $f(x)=-6|x + 5|-2$?\nthe graph of $f(x)$ is a horizontal compression of the graph of the parent function.\nthe graph of $f(x)$ is a horizontal stretch of the graph of the parent function.\nthe graph of $f(x)$ opens upward.\nthe graph of $f(x)$ opens to the right.

which statement is true about $f(x)=-6|x + 5|-2$?\nthe graph of $f(x)$ is a horizontal compression of the graph of the parent function.\nthe graph of $f(x)$ is a horizontal stretch of the graph of the parent function.\nthe graph of $f(x)$ opens upward.\nthe graph of $f(x)$ opens to the right.

Answer

Answer:

None of the given options are correct. The parent - function of (y = - 6|x + 5|-2) is (y = |x|). The graph of (y=-6|x + 5|-2) is a vertical stretch by a factor of 6, a reflection over the (x) - axis, a horizontal translation 5 units to the left, and a vertical translation 2 units down. The graph of (y = - 6|x+5|-2) opens downward (because of the negative coefficient (-6) in front of the absolute - value function).

Explanation:

Step1: Identify the parent function

The parent function of (y=-6|x + 5|-2) is (y = |x|).

Step2: Analyze the coefficient of the absolute - value

The coefficient (-6) causes a vertical stretch by a factor of 6 and a reflection over the (x) - axis. Since the coefficient is negative, the graph opens downward.

Step3: Analyze the horizontal and vertical translations

The (x+5) inside the absolute - value function causes a horizontal translation 5 units to the left, and the (-2) outside the absolute - value function causes a vertical translation 2 units down. There is no horizontal compression or stretch as there is no coefficient (a) inside the absolute - value function of the form (y = |ax|) ((a\neq1) and (a\neq - 1)) and the graph of an absolute - value function (y=a|x - h|+k) does not open to the right.