Question

In: Math

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

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

Solutions

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.


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

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