Problem

Use transformations to graph the function. \[ f(x)=-3|x+2|-1 \] Check

Solution

Step 1 :The function \(f(x)=-3|x+2|-1\) is a transformation of the absolute value function.

Step 2 :The absolute value function is reflected over the x-axis, stretched vertically by a factor of 3, shifted left by 2 units, and shifted down by 1 unit.

Step 3 :The graph of the function is a V-shaped graph that opens downwards, with the vertex at \((-2, -1)\).

Step 4 :\(\boxed{\text{The graph of the function } f(x)=-3|x+2|-1 \text{ is a reflection of the absolute value function, stretched vertically by a factor of 3, shifted left by 2 units, and shifted down by 1 unit.}}\)

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Source: https://solvelyapp.com/problems/6HlGqqeLUJ/

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