Answer:
Option a is correct
given data in the table represents an exponential function
The possible formula for the function is, ![y = f(x) = 12.5 (1.10)^x](https://tex.z-dn.net/?f=y%20%3D%20f%28x%29%20%3D%2012.5%20%281.10%29%5Ex)
An exponential function is in the form of
where a is the initial value and b ≠ 0 , b> 1.
Consider any two points from the table as shown;
(0, 12.5) and (1, 13.75)
Substitute these in [1] we have;
For (0, 12.5)
where x = 0 and f(x) = 12.5 in [1]
![12.5 = ab^0](https://tex.z-dn.net/?f=12.5%20%3D%20ab%5E0)
12.5 = a
For (1, 13.75)
![13.75 = ab^1](https://tex.z-dn.net/?f=13.75%20%3D%20ab%5E1)
13.75 = ab
Substitute the value of a =12.5 we have;
13.75 = 12.5b
divide both sides by 12.5 we get;
![b = \frac{13.75}{12.5} = 1.10](https://tex.z-dn.net/?f=b%20%3D%20%5Cfrac%7B13.75%7D%7B12.5%7D%20%3D%201.10)
since, y =f(x)
therefore, we have the following exponential function as:
![y= 12.5 (1.10)^x](https://tex.z-dn.net/?f=y%3D%2012.5%20%281.10%29%5Ex)
Answer:
a) reflection across the x-axis
b) f(x) =( x-3)²
c) f(x) = x² + 6 is a vertical taranslation up by '6' units
Step-by-step explanation:
<u>Explanation</u>
Given that the parent function
f(x) = x²
a) f(x) = x² is rotation across the x-axis then the new function
<em> f(x) = - x²</em>
b) ) f(x) = x² is a horizontal translation right by '3' units then the function is changes to <em>f(x) = (x-3)²</em>
c)
f(x) = x² is a vertical translation up '6' units then the function is changes to <em>f(x) = x² +6 </em>
Answer:
B or 2 topical
Step-by-step explanation:
Hope this helps :D
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Start with the last two choices.
You have x + 5 and x - 5 in the square root.
A square root can never be negative.
That means that the lowest value y can have in the last two choices is 0.
The range does not include -4.
Now look at choice B.
sqrt(x) is at least 0.
Then you add 5.
The range does not include -4.
Now look at choice A.
sqrt(x) is at least 0.
Now you subtract 5.
The lowest value y can have is -5. That includes -4.
Choice A is the answer.
y will be at least 5.