For the following exercises, use the graphs to write an equation for the function.

Expert Solution

Consider the graph given in exercise.

The graph appears to have x-intercepts at x = 2. At this, the graph passes through the intercept, suggesting linear factor.

The graph has two vertical asymptotes. The one at x = -3 showing the behavior of 1/x and the other at x = 4 showing the behavior of 1/x2.

So, this information can be used to write a function of the form given below,

f(x) = a(x – 2)/(x + 3)(x – 4)2.

To find the stretch factor, use a clear point on the graph, such as the y-intercept (0, 1) as shown below,

1 = a(0 – 2)/(0 + 3)(0 – 4)2

1 = a(-2/48)

1 = a(-1/24)

a = -24

So, the equation of the function in the graph is f(x) = -24(x – 2)/(x + 3)(x – 4)2.

Hafiz answered 11 months ago

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