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".