What effect does "a" have on the parent function y=1/x

1 answer:

7 0

Y=1/x is a reciprocal function & its shape is a special hyperbola with one branch located in the 1st Quadrant and the second in the 3dr Quadrant and both are symmetric about the origin O.
If a> 1 → y=a/x and the 2 branches are equally stretched upward & downward
about the center O.
If 0 < a < 1→y =a/x, the 2 branches are equally stretched downward and upward about the center O.
If a<0, then the 2 legs are in the 2nd and 4th Quadrant respectively

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Can someone help me and explain step by step

Shkiper50 [21]

Answer: 5) r = 5, 8th term = -78,125

6) r = 5, 8th term = -312,500

7) r = 5, {1, 5, 25, 125, 625}

8) r = 5, {-4, -20, -100, -500, -2500}

<u>Step-by-step explanation:</u>

The explicit formula of a geometric sequence is: $a_n=a_1\cdot r^{n-1}$ , where;

n is the number of the term
a₁ is the first term
r is the common ratio

$5)\ a_n=-5^{n-1}\\.\qquad =-1\cdot 5^{n-1}\quad \rightarrow \quad a_1=-1\ and\ r=5\\\\a_8=-5^{8-1}\\.\quad =-5^7\\.\quad =-78,125\\\\\\6)\ a_n=-4\cdot 5^{n-1}\quad \rightarrow \quad a_1=-4\ and\ r=5\\\\a_8=-4\cdot 5^{8-1}\\.\quad =-4\cdot 78,125\\.\quad =-312,500$

$7)\ a_1=1\ and\ r=5\\.\quad a_2=1\cdot 5=\boxed{5}\\.\quad a_3=5\cdot 5=\boxed{25}\\.\quad a_4=25\cdot 5=\boxed{125}\\.\quad a_5=125\cdot 5=\boxed{625}\\\\\\\\8)\ a_1=-4\ and\ r=5\\.\quad a_2=-4\cdot 5=\boxed{-20}\\.\quad a_3=-20\cdot 5=\boxed{-100}\\.\quad a_4=-100\cdot 5=\boxed{-500}\\.\quad a_5=-500\cdot 5=\boxed{-2500}\\\\\\$