How do you graph #y=-abs(x-8)+1#?

Answer 1

See below

#y=-abs(x-8)+1#

When approaching a graphing problem of this nature it may be easier to consider the following steps.

Step 1. The graph of #abs(x-8)# is the 'V-graph' formed as follows:
#f(x) = -(x-8)# for #x in (-oo, 8)# #f(8) = 0# #f(x) =+(x-8) # for #x in (8, +oo)#
Step 2. The graph of #-abs(x-8)# is the mirror reflection of the graph in Step 1 about the #x-#axis
Step 3. The graph of #-abs(x-8)+1# is the graph from Step 2 transformed ("shifted") 1 unit positive ("up") on the #y-#axis.
The resultant graph of #y# is shown below.

graph{-abs(x-8)+1 [-0.65, 11.84, -3.324, 2.92]}

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Answer 2

To graph the equation ( y = -\lvert x - 8 \rvert + 1 ), you can start by recognizing that it represents the absolute value function shifted horizontally by 8 units to the right and vertically by 1 unit upward. The vertex of the absolute value function is at the point (8, 1). Since the coefficient in front of the absolute value function is negative, the graph will be reflected over the x-axis.

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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.

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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