# How do you graph #f(x) =-2abs(4x-1)+16#?

Using the build in grapher we get

graph{-2abs(4x-1)+16 [-40, 40, -20, 20]}

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To graph the function ( f(x) = -2 \cdot |4x - 1| + 16 ), follow these steps:

- Identify the vertex of the absolute value function ( |4x - 1| ), which occurs when the expression inside the absolute value is equal to zero. So, solve ( 4x - 1 = 0 ) to find the x-coordinate of the vertex.
- Once you find the x-coordinate of the vertex, substitute it back into the original function to find the corresponding y-coordinate.
- Plot the vertex on the coordinate plane.
- Determine the direction of the absolute value function. Since the coefficient of ( |4x - 1| ) is negative (-2), the graph will open downwards.
- Choose a few points to the left and right of the vertex and plug them into the function to find their corresponding y-values.
- Plot these points on the graph.
- Connect the points smoothly to form the graph of the function.

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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