Questions: Graph this function: y=-3x-15

Graph this function: y=-3x-15
Transcript text: Graph this function: \[ y=|-3 x-15| \]
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Solution

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Solution Steps

Step 1: Identify the Function

The given function is \( y = |-3x - 15| \).

Step 2: Determine the Vertex

The vertex of the absolute value function \( y = |ax + b| \) occurs at the point where the expression inside the absolute value is zero. Therefore, we solve: \[ -3x - 15 = 0 \] \[ -3x = 15 \] \[ x = -5 \] Substituting \( x = -5 \) back into the function: \[ y = |-3(-5) - 15| = |15 - 15| = 0 \] Thus, the vertex is at the point \((-5, 0)\).

Step 3: Analyze the Function

The function \( y = |-3x - 15| \) is a V-shaped graph with the vertex at \((-5, 0)\). The slope of the lines forming the V is \(-3\) and \(3\).

Final Answer

The vertex of the function \( y = |-3x - 15| \) is at \((-5, 0)\).

{"axisType": 3, "coordSystem": {"xmin": -10, "xmax": 0, "ymin": 0, "ymax": 20}, "commands": ["y = abs(-3x - 15)"], "latex_expressions": ["$y = |-3x - 15|$"]}

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