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What is the graph of the absolute value function #f(x) = 4 | x | – 2#?

Answer 1

The graph of #f(x)# is the standard "V" graph of #absx# scaled by 4 units and shifted 2 units negative ("down") on the #y-#axis.

#f(x) =4absx-2#

Let's first consider the "parent" graph #y=absx#

This is the standard "V" graph shown below:

graph{absx [-10, 10, -5, 5]}

Now, #f(x)# is this standard graph scaled by 4 units and shifted 2 units negative ("down") on the #y-#axis. As below:

graph{4absx-2 [-10, 10, -5, 5]}

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Answer 2

Kennedy Adams

The graph of the absolute value function ( f(x) = 4 | x | - 2 ) is a V-shaped graph opening upwards, with the vertex at the point (0, -2) and the slope of each branch being 4.

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Answer from HIX Tutor

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.