Step-by-step explanation:
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)
[tex]\frac{0}{-1} = \frac{-ln (x - 4)}{-1}[/tex]
0 = ln (x - 4)
[tex]e^{0} = e^{ln (x - 4)}[/tex]
1 = x - 4
+4 +4
5 = x
(5, 0)
(???, 1): 1 = - ln (x - 4)
[tex]\frac{0}{-1} = \frac{-ln (x - 4)}{-1}[/tex]
1 = ln (x - 4)
[tex]e^{1} = e^{ln (x - 4)}[/tex]
e = x - 4
+4 +4
e + 4 = x
6.72 = x
(6.72, 1)
Domain: x - 4 > 0
+4 +4
x > 4
(4, ∞)
Vertical asymptotes: there are no vertical asymptotes for the parent function and the transformation did not alter that
No vertical asymptotes
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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 (explanation above)
