Write an equation for a graph that takes h(x)= ln(x) and reflects it over the y-axis, horizontally stretches it by a factor of 6, vertically shrinks it by a factor of 10, and moves it up 1 and 3 left

Answer 1

ln(x) --- reflects over y axis--> ln(-x) [reflection of f(x) over y axix is f(-x)]

-- horizontal stretch by a factor 6 -> ln(-x/6) [ horizontal stretch by m of f(x) is f(x/m) ]

---vertical shrink by a factor of 10 --> (1/10)ln(-x/6) [ vertical shrink of f(x) by a factor of s is (1/s) f(x) ]

-- moves it by 1 up-----------------> (1/10)ln(-x/6) +1 [ upward translation of f(x) by u is f(x) +u ]

---- moves 3 left ------------------->(1/10)ln(-(x+3)/6) +1 [left translation of f(x) by k is f(x+k) ]

i.e new function is 0.1ln(-0.5 - x/6) + 1

Answer 2

(1/10) ln (-(x+3)/6) + 1