Given the parent function f(x) = log2x, what is the equation of the function shown in the graph?

We have to choose what is the equation of the function on the graph. We know the parent function: f(x) = log(2) x ( log base 2 ). The new function should be in the form: f(x) = log(2) ( x - a ) + b. The new vertical asymptote is : x = -3, So: a = -3. Now we have: f (x) = log(2)( x + 3 ) + b. After that we will substitute the values of coordinates of the point ( - 5 , - 2 ) which belong to this function. - 5 = log(2) ( - 2 + 3 ) + b. - 5 = log (2) 1 + b ; - 5 = 0 + b; b = - 5. The equation of the function shown in the graph is: A ) f (x) = log(2) ( x + 3 ) - 5 .

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