Question

Help please!!!!!!!!!

Answer 1

Answer:

(a)  3.5

(b)  x = 4

(c)  -¹/₂

(d)  -¹/₂

Step-by-step explanation:

Part (a)

f(1) is the value of y when x = 1.

To find the value of y from a given value of x, find the position of x on the x-axis, then trace vertically until you meet the line. Once you meet the line, trace horizontally to the y-axis to find the corresponding value of y.

Therefore, f(1) = 3.5.

Part (b)

To solve f(x) = 2, find the value of x when y = 2.

To find the value of x from a given value of y, find the position of y on the y-axis, then trace horizontally until you meet the line. Once you meet the line, trace vertically to the x-axis to find the corresponding value of x.

Therefore, the solution of f(x) = 2 is x = 4.

Part (c)

The average rate of change of function f(x) over the interval a ≤ x ≤ b is given by:

$\dfrac{f(b)-f(a)}{b-a}$

Given interval:  2 ≤ x ≤ 4

Therefore:

• a = 2
• b = 4

$\implies \dfrac{f(4)-f(2)}{4-2}=\dfrac{2-3}{4-2}=-\dfrac{1}{2}$

Part (d)

The average rate of change between any interval of the given function will be the same as the graph is linear.  Therefore, the average rate of change from 0 to 8 is the same as the rate found in part (c):  -¹/₂.

Proof

The average rate of change of function f(x) over the interval a ≤ x ≤ b is given by:

$\dfrac{f(b)-f(a)}{b-a}$

Given interval:  0 ≤ x ≤ 8

Therefore:

• a = 0
• b = 8

$\implies \dfrac{f(8)-f(0)}{8-0}=\dfrac{0-4}{8-0}=-\dfrac{4}{8}=-\dfrac{1}{2}$