Question

Given the graph below, determine the values for a and b in the equation y=blog_5(x+a) . If a value is a non-integer then type it as a reduced fraction.vert asymp at x=1.as x goes to 1 f(x) goes to -infinity.as x goes to infinity f(x) goes to infinity. (6,1) is on graphThe value for a is AnswerThe value for b is Answer

Answer 1

For this problem we were given a logaritmic function of the type:

$y=b\cdot\log _5(x+a)$

And its graph. From that we need to determine the values of "b" and "a".

From the graph we can notice two important points (6,1) and (2,0). If we replace the coordinates for these two points on the expression for the function, we can determine the values of b and a. This is done below:

$\begin{gathered} 0=b\cdot\log _5(2+a) \\ \log _5(2+a)=0 \\ 5^{\log _5(2+a)}=5^0 \\ 2+a=1 \\ a=1-2 \\ a=-1 \end{gathered}$

From the first point, we can conclude that "a" is equal to -1. From that, we can find the value of b using the second point:

$\begin{gathered} 1=b\cdot\log _5(6-1) \\ 1=b\cdot\log _55 \\ b\cdot1=1 \\ b=1 \end{gathered}$

The value for a is -1.

The value for b is 1.