Question

The table of values represents a quadratic function.

Answer 1

Answer:

The average rate of change for f(x) from x=−5 to x = 10 is, 11

Step-by-step explanation:

Average rate A(x) of change for a function f(x) over [a, b] is given by:

$A(x) = \frac{f(b)-f(a)}{b-a}$

As per the statement:

We have to find the average rate of change for f(x) from x=−5 to x = 10.

From the table we have;

At x = -5

f(-5) = 39

and

at x = 10

f(10) = 204

Substitute these in [1] we have;

$A(x) = \frac{f(10)-f(-5)}{10-(-5)}$

⇒$A(x) = \frac{204-39}{10+5}$

⇒$A(x) = \frac{165}{15}$

Simplify:

A(x) = 15

Therefore, the average rate of change for f(x) from x=−5 to x = 10 is, 11

Answer 2

$\bf \begin{array}{rrllll} x&f(x)\\ \textendash\textendash\textendash\textendash\textendash\textendash&\textendash\textendash\textendash\textendash\textendash\textendash\\ -10&184\\ \boxed{-5}&\boxed{39}\\ 0&-6\\ 5&49\\ \boxed{10}&\boxed{204} \end{array} \\\\\\ \\\\\\ \cfrac{f(x_2)-f(x_1)}{x_2-x_1}\impliedby \textit{average rate of change} \\\\\\ \cfrac{f(10)-f(-5)}{10-(-5)}\implies \cfrac{f(10)-f(-5)}{10+5}\implies \cfrac{\boxed{204}-\boxed{39}}{10+5} \\\\\\ \cfrac{165}{15}\implies 11$