Give a formula for the function illustrated using a vertical shift of an exponential function. The two points marked on the graph are A=(−2,10) and B=(2,4)The red horizontal line is given by
y =2 and is a horizontal asymptote of the function.
clearly, the vertical shift is 2, since all y = a^x have a horizontal asymptote of y=0.
So now we can assume that
y = a*b^x and
a/b^2 = 8
ab^2 = 2
a =4
b^2 = 1/2
y = 4*2^(-x/2) + 2
Give a formula for the function illustrated using a vertical shift of an exponential function. The two points marked on the graph are 𝐴=(−1,29)
and 𝐵=(1,5)
. The red horizontal line is given by 𝑦=4
, and is a horizontal asymptote of the function.