X
∈
R
,
x
≠
±
2
y
∈
R
,
y
≠
1
Explanation:
The denominator of f(x) cannot be zero as this would make f(x) undefined. Equating the denominator to zero and solving gives the values that x cannot be.
solve
x
2
−
4
=
0
⇒
x
2
=
4
⇒
x
=
±
2
←
excluded values
⇒
domain is
x
∈
R
,
x
≠
±
2
To find the value that y cannot be find
lim
x
→
±
∞
f
(
x
)
divide terms on numerator/denominator by the highest power of x, that is
x
2
f
(
x
)
=
x
2
x
2
−
2
x
2
x
2
x
2
−
4
x
2
=
1
−
2
x
2
1
−
4
x
2
as
x
→
±
∞
,
f
(
x
)
→
1
−
0
1
−
0
⇒
y
→
1
←
excluded value
⇒
range is
y
∈
R
,
y
≠
1
The graph of f(x) illustrates this.
graph{(x^2-2)/(x^2-4) [-10, 10, -5, 5]}
No because the scale factors are different. You can see that QR compared to VT the scale factor is 2, but in RS and TU it's different, so they are not similar.
<span>To find the original dimensions, write a proportion with the scale as the first ratio and the scale dimension compared to the actual dimension as the second ratio. Use cross products to solve. To find new dimensions, write a proportion with the new scale as the first ratio and the scale dimension compared to the actual dimension as the second ratio. Use cross products to solve.</span>
The rate of change is the decrease in altitude per change in two seconds
![\begin{gathered} \frac{3}{8}\text{ divided by 2} \\ \frac{3}{8}\text{ x}\frac{1}{2} \\ \Rightarrow\frac{3}{16}ft\text{ per second} \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20%5Cfrac%7B3%7D%7B8%7D%5Ctext%7B%20divided%20by%202%7D%20%5C%5C%20%5Cfrac%7B3%7D%7B8%7D%5Ctext%7B%20x%7D%5Cfrac%7B1%7D%7B2%7D%20%5C%5C%20%5CRightarrow%5Cfrac%7B3%7D%7B16%7Dft%5Ctext%7B%20per%20second%7D%20%5Cend%7Bgathered%7D)
If the initial altitude is y ft
The most profitable investment for a candy shop that earns $1 profit per pound of candy is "Machine with $8 per hour operating cost, producing 14 pounds of candy per hour".<span>
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