Which is the graph of y = -1/x?
1 answer:
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The iterative rule for the sequence is a_n = 8 · ( 0.5 )ⁿ ⁻ ¹
<h3>Further explanation</h3>Firstly , let us learn about types of sequence in mathematics.
Arithmetic Progression is a sequence of numbers in which each of adjacent numbers have a constant difference.
<em>Tn = n-th term of the sequence</em>
<em>Sn = sum of the first n numbers of the sequence</em>
<em>a = the initial term of the sequence</em>
<em>d = common difference between adjacent numbers</em>
Geometric Progression is a sequence of numbers in which each of adjacent numbers have a constant ration.
<em>Tn = n-th term of the sequence</em>
<em>Sn = sum of the first n numbers of the sequence</em>
<em>a = the initial term of the sequence</em>
<em>r = common ratio between adjacent numbers</em>
Let us now tackle the problem!
<u>Given:</u>
a₁ = 8
a₂ = 4
a₃ = 2
a₄ = 1
<u>Solution:</u>
<em>Firstly , we find the ratio by following formula:</em>
<em>The iterative rule for the sequence:</em>
- Geometric Series : brainly.com/question/4520950
- Arithmetic Progression : brainly.com/question/2966265
- Geometric Sequence : brainly.com/question/2166405
Grade: Middle School
Subject: Mathematics
Chapter: Arithmetic and Geometric Series
Keywords: Arithmetic , Geometric , Series , Sequence , Difference , Term
Answer:
f(x) = -19/9(x + 3)² + 5
Step-by-step explanation:
Given the vertex, (-3, 5) and the point, (0, 14):
Use the following quadratic equation formula in vertex form:
f(x) = a(x - h)² + k
where:
(h, k) = vertex
a = determines whether the graph opens up or down, and makes the graph wide or narrow.
<em>h</em><em> </em>= determines how far left or right the parent function is translated.
<em>k</em> = determines how far up or down the parent function is translated.
Plug in the values of the vertex, (-3, 5) and the given point, (0, 14) to solve for <em>a</em>:
f(x) = a(x - h)² + k
14 = a(0 + 3)² + 5
14 = a(3)² + 5
14 = a(9) + 5
Subtract 5 from both sides:
-14 - 5 = 9a
-19 = 9a
Divide both sides by 9 to solve for a:
-19/9 = 9a/9
-19/9 = a
Therefore, the quadratic function in vertex form is:
f(x) = -19/9(x + 3)² + 5
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