S = n(a1 + an)/2
2S = n(a1 + an)
2S = na1 + nan
nan = 2S - na1
an = (2S - n a1)/n
<u>Step-by-step explanation:</u>
transform the parent graph of f(x) = ln x into f(x) = - ln (x - 4) by shifting the parent graph 4 units to the right and reflecting over the x-axis
(???, 0): 0 = - ln (x - 4)

0 = ln (x - 4)

1 = x - 4
<u> +4 </u> <u> +4 </u>
5 = x
(5, 0)
(???, 1): 1 = - ln (x - 4)

1 = ln (x - 4)

e = x - 4
<u> +4 </u> <u> +4 </u>
e + 4 = x
6.72 = x
(6.72, 1)
Domain: x - 4 > 0
<u> +4 </u> <u>+4 </u>
x > 4
(4, ∞)
Vertical asymptotes: there are no vertical asymptotes for the parent function and the transformation did not alter that
No vertical asymptotes
*************************************************************************
transform the parent graph of f(x) = 3ˣ into f(x) = - 3ˣ⁺⁵ by shifting the parent graph 5 units to the left and reflecting over the x-axis
Domain: there is no restriction on x so domain is all real number
(-∞, ∞)
Range: there is a horizontal asymptote for the parent graph of y = 0 with range of y > 0. the transformation is a reflection over the x-axis so the horizontal asymptote is the same (y = 0) but the range changed to y < 0.
(-∞, 0)
Y-intercept is when x = 0:
f(x) = - 3ˣ⁺⁵
= - 3⁰⁺⁵
= - 3⁵
= -243
Horizontal Asymptote: y = 0 <em>(explanation above)</em>
<em><u>Step</u></em><em><u>•</u></em><em><u>BY</u></em><em><u>•</u></em><em><u>Step</u></em><em><u> </u></em><em><u>Explanation</u></em><em><u>~</u></em><em><u>|</u></em>
<em><u> </u></em><em><u>♡</u></em><em><u>♡</u></em><em><u>♡</u></em><em><u>♡</u></em><em><u>♡</u></em><em><u>♡</u></em><em><u>♡</u></em><em><u>♡</u></em><em><u>♡</u></em><em><u>♡</u></em><em><u>♡</u></em><em><u>♡</u></em><em><u>♡</u></em><em><u> </u></em><em><u> </u></em><em><u> </u></em><em><u> </u></em><em><u> </u></em>
y=1.50
x=0.50
¹
1.50
1.59
______+
3.00
0.50
_____+
<em>3.50</em>
<h2>
<em><u>Answer</u></em><em><u>:</u></em><em><u>♡</u></em><em><u>~</u></em></h2>
<em><u>3.50</u></em>
<em><u>HOPE</u></em><em><u> </u></em><em><u>IT</u></em><em><u> </u></em><em><u>HELPSS</u></em>