What is the range of the function f(x) = 3/4 |x|-3 a, all real numbers b. all real numbers less than or equal to 3 c. all real numbers less than or equal to –3 d. all real numbers greater than or equal to –3

The range of the function f(x) = 3/4 |x|-3 is [-3, ) and this can be determined by using the graph of the given function.

Given :

Function  -- f(x) = 3/4|x| - 3

The steps can be used in order to determine the range of the function:

Step 1 - Write the given function.

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

Step 2 - Draw the graph of (y = x).

Step 3 - Now, take the mirror image of the graph obtained in the above step. So, the graph obtained is the graph of (y = |x|).

Step 4 - Now, multiply the y-axis by 3/4. So, the graph obtained is the graph of (y = 3/4|x|).

Step 5 - Now, translate the graph obtained in the above step in the downward direction by a factor of 3. So, the graph obtained is the graph of (y = 3/4|x| - 3).

Step 6 - From the graph obtained in the above step, it can be concluded that the range of the function is [-3, ).

Therefore, the correct option is D).

For more information, refer to the link given below:

link

hope it you

step-by-step explanation:

sin(7pi/6 - pi/3)  

= sin(7pi/6 - 2pi/6)  

= sin(5pi/6)  

= sin(pi - pi/6)  

= sin(pi/6)  

= 1/2  

sin 7pi/6 - sin pi/3  

= sin (pi + pi/6) - sin pi/3  

= -sin pi/6 - sin pi/3  

= -1/2 - sqrt(3)/2  

= -(1+sqrt(3))2