(2. Given g(x) = -2 5x², find g(8ax)
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Given this equation:
That represents t<span>he height of a tree in feet over (x) years. Let's analyze each statement according to figure 1 that shows the graph of this equation.
</span>
The tree's maximum height is limited to 30 ft.
As shown in figure below, the tree is not limited, so this statement is false.
<span>The tree is initially 2 ft tall
The tree was planted in x = 0, so evaluating the function for this value, we have:
</span>
<span>
<span>So, the tree is initially
tall.
</span>
Therefore this statement is false.
</span>Between the 5th and 7th years, the tree grows approximately 7 ft.
<span>
if x = 5 then:
</span>
<span>
</span>if x = 7 then:
So, between the 5th and 7th years the height of the tree remains constant
:
This is also a false statement.
<span>After growing 15 ft, the tree's rate of growth decreases.</span>
It is reasonable to think that the height of this tree finally will be 301ft. Why? well, if x grows without bound, then the term
approaches zero.
Therefore this statement is also false.
Conclusion: After being planted this tree won't grow.
That represents t<span>he height of a tree in feet over (x) years. Let's analyze each statement according to figure 1 that shows the graph of this equation.
</span>
The tree's maximum height is limited to 30 ft.
As shown in figure below, the tree is not limited, so this statement is false.
<span>The tree is initially 2 ft tall
The tree was planted in x = 0, so evaluating the function for this value, we have:
</span>
<span>
<span>So, the tree is initially
</span>
Therefore this statement is false.
</span>Between the 5th and 7th years, the tree grows approximately 7 ft.
<span>
if x = 5 then:
</span>
</span>if x = 7 then:
So, between the 5th and 7th years the height of the tree remains constant
:
This is also a false statement.
<span>After growing 15 ft, the tree's rate of growth decreases.</span>
It is reasonable to think that the height of this tree finally will be 301ft. Why? well, if x grows without bound, then the term
Therefore this statement is also false.
Conclusion: After being planted this tree won't grow.