The nth term of a sequence is 3n+4 explain why 21 is not a term of this sequence

1 answer:

6 0

In this sequence, n can only be a natural number. So, if you plug in 5 for n, then you get 19. Also, if you plug in 6 for n, you get 24. Since no natural number can be replaced with n to get 21, it isn’t a term in the sequence

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The graph of f(x)=cos(x) is transformed to a new function, g(x) , by stretching it horizontally by a factor of 4 and shifting it

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The equation of the new function is $g(x)= cos4 x+1$

Explanation:

The Parent function is $f(x)=cos x$

We need to determine the new function g(x) using the transformation by stretching the f(x) horizontally by a factor of 4 and shifting it 1 unit up.

The function transformation formula is given by

$f(x)=a \cos b(x-c)+d$

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b compresses or stretches it horizontally,

c shifts the function left or right

d shifts the function up or down

Since, it is given that the function stretches horizontally by a factor of 4 and shifting it 1 unit up.

Hence, $b=4$ and $d=1$

Substituting these values in the formula, we have,

$g(x)=cos4x+1$

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