Question

What is the range of the function f(x)=3/4 |x|-3

All real numbers
All real numbers less then or equal to 3
All real numbers less than or equal to -3
All real numbers greater than or equal to -3​

Answer 1

The answer is the forth one.

Answer 2

The range of the given function is:

• All real numbers greater than or equal to -3​

Explanation:

We are given a modulus function f(x) by:

`f(x)=(3)/(4)|x|-3`

From the graph of the function we may see that the graph continuously decreases from x= ∞ to x=0 and at x=0 the function attains the values ,

f(0)= -3

and then it again increases continuously and goes to infinity.

Hence, the function covers all the real values between -3 to ∞

i.e. The range of the function in interval form is: [-3,∞)

Hence, the answer is:

All real numbers greater than or equal to -3​