Question

Which graph represents the function f(x) = 4|x|?

Answer 1

we have

$y=4\left|x\right|$

using a graph tool

see the attached figure

1) the domain of the function is all real numbers------> (-∞,∞)

2) the range of the function is the interval------> [0,∞)

3) the function decrease in the interval (-∞,0)

4) the function increase in the interval (0,∞)

therefore

the answer in the attached figure

Answer 2

Answer:

The graph of the given function : f(x) = 4|x| is attached below :

Before plotting the graph fir finding the nature of the function f(x) such as Domain, Range, Intervals of increasing and Decreasing of the function.

1) Domain : Since |x| can take any real value so the domain of the given function 4|x| is every real number.

⇒ Domain of 4|x| = (-∞,∞)

2) Since, the absolute value function only gives positive value and 0. So the Range of the function is every positive real number including 0

⇒ Range of 4|x| = [0,∞)

3) If we check the value of 4x when x<0 then the value is negative

⇒ The function 4|x| is decreasing in the interval (-∞,0]

4) If we check the value of 4x when x>0 then the value is positive

⇒ The function 4|x| is increasing in the interval [0,∞)