For the following exercises, use the graphs to write a polynomial function of least degree.

Expert Solution

Consider the graph provided in the exercise.

Start from left,

The first zero occurs at x = -2/3. It is crossing x-axis linearly so it has multiplicity of 1.

The second zero occurs at x = 0.5. It is crossing x-axis linearly so it has multiplicity of 1.

The third zero occurs at x = 4/3. It is crossing x-axis linearly so it has multiplicity of 1.

Combine all this,

f(x) = a(x + 2/3)(x – 1/2)(x – 4/3)

To determine stretch factor a, put y intercept (0, 8) in the equation.

8 = a(0 + 2/3)(0 – 1/2)(0 – 4/3)

8 = a4/9

a = 72/4

a = 18

Hence, the function is f(x) = 18(x + 2/3)(x – 1/2)(x – 4/3).

Junaid answered 1 year ago

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