Question

Without using a calculator, determine if each each of the following functions is increasing or decresing on the interval x= 1 to x= 2 a. g(x) = 40 – 2 b. f (x) = 3x C. h(x) = 2 - X

Answer 1

Answer:

a. Increasing

b. Increasing

c. Decreasing

Explanation:

Part A (g(x) = 4x – 2)

$\begin{gathered} g(2)=4(2)-2=8-2=6 \\ g(1)=4(1)-2=4-2=2 \\ \frac{g(2)-g(1)}{2-1}=\frac{6-2}{1} \\ =\frac{4}{1} \\ =4 \end{gathered}$

g(x) is increasing since its rate of change is positive.

Part B (f(x) = 3x)

$\begin{gathered} f(2)=3(2)=6 \\ f(1)=3(1)=3 \\ \frac{f(2)-f(1)}{2-1}=\frac{6-3}{1} \\ =\frac{3}{1} \\ =3 \end{gathered}$

f(x) is increasing since its rate of change is positive.

Part C (h(x) = 2-x)

$\begin{gathered} h(2)=2-2=0 \\ h(1)=2-1=1 \\ \frac{h(2)-h(1)}{2-1}=\frac{0-1}{1} \\ =\frac{-1}{1} \\ =-1 \end{gathered}$

h(x) is decreasing since its rate of change is negative.