Problem

Suppose the function $f$ is updated from $f(x)=x^{5}$ to $f(x)=-0.6 x^{5}$. How does changing the coefficient from 1 to -0.6 impact the output of the function? Select all that apply.
The output value gets further from 0 .
The output value gets closer to 0 .
The sign of the output changes.
The function is no longer a monomial function.

Answer

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Answer

Therefore, the changes are: The output value gets closer to 0 and the sign of the output changes.

Steps

Step 1 :First, let's understand the function $f(x)=x^{5}$. This is a monomial function where the output value increases as $x$ increases.

Step 2 :Now, the function is updated to $f(x)=-0.6 x^{5}$. The coefficient of $x^{5}$ changes from 1 to -0.6. This means that the output of the function will be multiplied by -0.6.

Step 3 :This change will have two effects. First, the output value will get closer to 0 because multiplying by a fraction (in this case -0.6) reduces the magnitude of the number.

Step 4 :Second, the sign of the output will change. This is because multiplying by a negative number changes the sign of the number.

Step 5 :However, the function is still a monomial function because it still has only one term, which is $-0.6 x^{5}$.

Step 6 :Therefore, the changes are: The output value gets closer to 0 and the sign of the output changes.

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