The graph of f(x) = x2 is translated to form g(x) = (x – 5)2 + 1.Which graph represents g(x)?
2 answers:
The graph of and the graph of
. These two graphs are illustrated in the Figure bellow. So, let's explain what this means:
- For a function f(x), a new function g(x) = f(x - c) represents to shift the graph <em>c</em> units to the right.
- For a function f(x), a new function g(x) = f(x) + k represents to shift the graph <em>k</em> units upward.
Since in our problem the function g(x) = f(x - c) + k, we have shifted the function f(x) <em>c </em>units to the right and <em>k </em>units upward, that is, we have shifted the function f(x) <em>5 </em>units to the right and <em>1 </em>unit upward as indicated in the Figure bellow.
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<em><u>The recursive formula to find nth term of sequence is:</u></em>
and n = 1, 2, 3, ....
<em><u>Solution:</u></em>
Given a sequence is:
3, 7, 11, 15, 19, 23, 27, 31, 35
<em><u>Let us find the difference between terms</u></em>
7 - 3 = 4
11 - 7 = 4
15 - 11 = 4
19 - 15 = 4
23 - 19 = 4
27 - 23 = 4
31 - 27 = 4
35 - 31 = 4
Thus the difference between terms is constant
Thus the given sequence is arithmetic sequence
An arithmetic sequence is a sequence of numbers such that the difference of any two successive members of the sequence is a constant
<em><u>The nth term of arithmetic sequence is given by:</u></em>
= the nᵗʰ term in the sequence
= the first term in the sequence
d = the common difference between terms
Here in the given sequence
d = 4
Substitute in above formula,
<em><u>Thus the recursive formula to find nth term of sequence is:</u></em>
and n = 1, 2, 3, ......