Question

Write an equation for the transformed logarithm shown below, that passes through (-3,0) and (2,-2).

Answer 1

given points are (-3,0) & (2,-2) where general form of the function is f@) = -a logor) +K - a: scale of the logarithmic graph K: whether the graph is shifted down or up negative sign indicates that the graph is reflected along the x-axis The vertical asymptote is at x=-4 so ear o f(x) = -a log(x+4) +R — ☺ The (x+4) is the part of the above equation shows that the graph is shifted & 4 Units toward left for K 4a: fork, plug in the point (-3,0) in 0 = -a log 1-3 +4h+k ③ > 0 = -AX0 + R . for a plug in the point (2,-2) & the value of kao in equ O -2=-a log(2+4) +0 ogle +

So from egn ③ put a ak flu) Vegion 1 ang lx #6) +0 fla) = -2 log (x+4) log(6) or in compact form: f(a) = - 2 log(x+4)