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1 answer:
Answer:
<em>D. y = -6x + 38</em>
Step-by-step explanation:
<u>Equation of a sequence</u>
We are given the following sequence of numbers corresponding to the positions x={1,2,3,4,5,...}
y={32,26,20,14,8....}
To find the equation of the sequence, we must recall the general term of a sequence is:
Where r is the common difference between two consecutive terms, an and a1 are the x-th and the first terms respectively.
We can find the value of r by subtracting any pair of consecutive terms:
r = 26-32 = 20-26 = 14-20 = -6
Now we apply the formula:
y=32+(x-1).(-6)
Operating:
y=32-6x+6
y = -6x + 38
Answer:
D. y = -6x + 38
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Using translation concepts, the graph of g(x) = 3x² + 1 is given at the end of the answer.
<h3>What is a translation?</h3>A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction either in it’s definition or in it’s domain. Examples are shift left/right or bottom/up, vertical or horizontal stretching or compression, and reflections over the x-axis or the y-axis.
For this problem, we have that the parent function is:
f(x) = x².
The shifted function is:
g(x) = 3x² + 1.
The transformations are given as follows:
- It was vertically compressed by a factor of 3, due to the multiplication by 3.
- It was shifted up 1 unit, due to the addition of 1.
In the graph at the end of the answer, both functions are shown, with <u>f(x) in red and g(x) in blue</u>.
More can be learned about translation concepts at brainly.com/question/28393734
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