How to classify each function as increasing, decreasing, or constant?

Question

A. F(x)= 0.1 

B. F(x)= 2/5x, where x is an integer 

C. F(x)= -4x 

D. F(x)= 7x

Answer 1

A) The function f(x) = 0.1

Replace f(x) to y.

y = 0.1

The above function represents a horizontal line.

Horizontal line is a constant function.

f(x) = 0.1 is constant function.

 

B) The function

Change f(x) to y.

• For x = 1

• For x = 2

In this case the x values are 1 < 2, Then y values are 0.4 > 0.2.

A function is "decreasing" when the y value decreases as the x value increases.

The function is decreasing function.

Answer 2

C) The function f(x) = - 4x

Change f(x) to y.

y = - 4x

• For x = 1

y = - 4(1)

y = - 4

• For x = 2

y = - 4(2)

y = - 8

In this case the x values are 1 < 2, Then y values are - 4 > - 8.

A function is "decreasing" when the y value decreases as the x value increases.

The function f(x) = - 4x is decreasing function.

D) The  function f(x) = 7x

y = 7x

• For x = 1

y = 7(1)

y = 7

• For x = 2

y = 7(2)

y = 14

In this case the x values are 1 < 2, Then y values are 7 < 14.

A function is "increasing" when the y value increases as the x value increases.

The function f(x) =7x is increasing function.