Questions: Graph the equation shown below by transforming the given graph of the parent function. y=--x-4

Graph the equation shown below by transforming the given graph of the parent function. y=--x-4
Transcript text: Graph the equation shown below by transforming the given graph of the parent function. \[ y=-|-x|-4 \]
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Solution

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Solution Steps

Step 1: Reflect across the y-axis

The graph of $y = |-x|$ is the same as $y = |x|$ because the absolute value of a negative number is the same as the absolute value of the positive version of that same number. So, reflecting $|x|$ over the y-axis results in the same graph.

Step 2: Reflect across the x-axis

The graph of $y = -|x|$ is obtained by reflecting the graph of $y=|x|$ across the x-axis. This means that if a point $(x, y)$ is on the graph of $y = |x|$, then the point $(x, -y)$ is on the graph of $y = -|x|$.

Step 3: Vertical Translation

The graph of $y = -|x| - 4$ is obtained by shifting the graph of $y = -|x|$ down by 4 units. This means that if a point $(x, y)$ is on the graph of $y = -|x|$, then the point $(x, y - 4)$ is on the graph of $y = -|x| - 4$.

Final Answer:

The final graph of $y = -|-x|-4$ or $y = -|x| - 4$ is the graph of $y=|x|$ reflected over the x-axis and shifted down 4 units. The vertex is at $(0,-4)$. The graph passes through points $(1, -5)$, $(-1, -5)$, $(2,-6)$, $(-2, -6)$, etc.

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