When answering things like this do the brackets first, is there are parenthesis in the brackets do those but keep it in the brackets and work regularly after
Please help and thank you.
1 answer:
Answer:
s(x) is t(x) ...
- horizontally compressed by a factor of 2,
- reflected across the y-axis, and
- translated downward 5 units.
Domain and Range
- t(x) has a domain of x ≤ 0, and a range of y ≥ 0.
- s(x) has a domain of x ≥ 0, and a range of y ≥ -5.
Step-by-step explanation:
t(x) is the square root function reflected across the y-axis and compressed horizontally by a factor of 2. That is, in f(x) = √x, the x has been replaced by -2x.
s(x) has the function t(x) <em>reflected back across the y-axis</em> and compressed horizontally by another factor of 2. It is also <em>translated downward by 5 units</em>, so that its origin (vertex) is at (0, -5).
_____
The graph shows you the domain and range of s(x). The domain is all numbers to the right of x=0, including x=0. That is ...
domain: x ≥ 0
The range is all numbers -5 or above:
range: y ≥ -5
___
For t(x), the argument of the square root function must not be negative, which means the value of x cannot be positive.
domain: x ≤ 0
For non-negative values of radicand, the t(x) function will have non-negative values. So, the range is ...
range: y ≥ 0
_____
<em>Comment on solving problems like this</em>
Your graphing calculator can be your friend.
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Answer:
The time it will take the population to grow to 800 insects is 17 days.
Step-by-step explanation:
The growth function of the insects is exponential.
The exponential growth function is:
Here,
<em>y</em> = final value
<em>a</em> = initial value
<em>r</em> = growth rate
<em>t</em> = time taken
It is provided that there were 270 insects after 9 days and initially there were 80 insects.
Compute the value of <em>r</em> as follows:
Now, compute the time it will take the population to grow to 800 insects as follows:
Thus, the time it will take the population to grow to 800 insects is 17 days.