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Describe ALL of the key features. (Question and photo are below)

Describe ALL of the key features. (Question and photo are below)-example-1
User Zilk
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1 Answer

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Part (a)

The intercepts are where the graph crosses and x and y axis.

The x intercept is located at (2,0). As shorthand, we can state "The x intercept is 2" because the y coordinate is always 0.

The y intercept is 2 and it's at the location (0,2)

Summary

x intercept = 2

y intercept = 2

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Part (b)

The positive interval is when the line or curve is above the x axis.

This happens when x < 2 or -∞ < x < 2

That second inequality converts to the interval notation (-∞, 2)

The parenthesis means we exclude the endpoint 2.

The negative interval is when x > 2 or 2 < x or 2 < x < ∞

The last inequality mentioned converts to the interval notation (2, ∞)

Summary:

Positive interval is (-∞, 2)

Negative interval is (2, ∞)

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Part (c)

The entire graph slopes downhill as we move to the right. Therefore, this function is never increasing. It is always decreasing.

Increasing interval = none

Decreasing interval = entire real number line = (-∞, ∞)

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Part (d)

Informally, the end behavior is "rises to the left, falls to the right".

  • "Rises to the left" means as x → -∞, then y → ∞
  • "Falls to the right" means as x → ∞, then y → -∞

Notice how x and y move toward opposite infinities. This will apply to any odd function. By "odd", I mean in terms of "even and odd".

User Izack
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