Question

Given the parent function g(x)=log2(x), what is the equation of the function shown in the graph ?

Answer 1

Answer:The equation of the function shown in the graph is: A ) f (x) = log(2) ( x + 3 ) - 5 .

Step-by-step explanation: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.

Answer 2

The equation of the function shown in the graph is f(x) = log₂(x + 4) - 1

How to determine the equation of the function shown in the graph

From the question, we have the following parameters that can be used in our computation:

The graph

Where, we have

g(x) = log₂(x)

First, the function is shifted to the left by 4 units

So, we have

g(x) = log₂(x + 4)

Next, the function is shifted down by 1 unit

So, we have

f(x) = log₂(x + 4) - 1

Hence, the equation of the function shown in the graph is f(x) = log₂(x + 4) - 1