calculate the average rate of change from ( x = - 2 ) to ( x = 1 ) of the function below.\n( f ( x ) = x ^ {…

calculate the average rate of change from ( x = - 2 ) to ( x = 1 ) of the function below.\n( f ( x ) = x ^ { 2 } + 5 x - 12 )\nfirst, find the change in ( y ) by evaluating the function at ( - 2 ) and ( 1 ):\n( f ( - 2 ) = )\n( f ( 1 ) = )\nthe change in ( y ) is

calculate the average rate of change from ( x = - 2 ) to ( x = 1 ) of the function below.\n( f ( x ) = x ^ { 2 } + 5 x - 12 )\nfirst, find the change in ( y ) by evaluating the function at ( - 2 ) and ( 1 ):\n( f ( - 2 ) = )\n( f ( 1 ) = )\nthe change in ( y ) is

Answer

Explanation:

Step1: Evaluate (f(-2))

Substitute (x = - 2) into (f(x)=x^{2}+5x - 12): [ \begin{align*} f(-2)&=(-2)^{2}+5\times(-2)-12\ &=4-10 - 12\ &=-18 \end{align*} ]

Step2: Evaluate (f(1))

Substitute (x = 1) into (f(x)=x^{2}+5x - 12): [ \begin{align*} f(1)&=1^{2}+5\times1-12\ &=1 + 5-12\ &=-6 \end{align*} ]

Step3: Calculate the change in (y)

The change in (y) is (f(1)-f(-2)). [ \begin{align*} f(1)-f(-2)&=-6-(-18)\ &=-6 + 18\ &=12 \end{align*} ]

Answer:

(f(-2)=-18), (f(1)=-6), the change in (y) is (12)