Question 1124548
your piece-wise functions are:


F(x)=3x+4 if-2<=x<0
-3 if x=0
-2x if x>0


the first of them is f(x) = 3x + 4 if -2 <= x < 0


let y = f(x).


the equation becomes y = 3x + 4 if -2 <= x < 0


the domain is all real values of x such that -2 <= x < 0


the range is all real values of y then x is equal to -2 all the way up to when x is < 0.


when x = -2, y = 3x + 4 = -2
when x = 0,y = 4


the range is therefore all real values of y such that -2 <= y < 4


the x-intercept is the value of x when y = 0.


when y = 0, the equation becomes 0 = 3x + 4


solve for x to get x = -4/3.


the x-intercept is -4/3, which is the point (-4/3, 0)


the y-intercept is the value of y when x = 0.


since x can't be equal to 0, there is no y-intercept.


the second of them is f(x) = -3 if x = 0.


let y = f(x) and the equation becomes y = -3.


the domain is all real values of x such that x = 0.


in other words, the value of x can only be 0.


the range is all real values of when hen x = 0.


the range is therefore all real values of y such that y = -3


in other words, the value of y can only be -3.


the x-intercept is the value of x when y = 0.


since y can't be equal to 0, there is no x-intercept.


the y-intercept is the value of y when x = 0.


the y-intercept is therefore y = -3 which is the point (0,-3).


the third of them is f(x) = -2x when x > 0.


let y = f(x) and the equation becomes y = -2x when x > 0


the domain is all real values of x such that x > 0


the range is all real values of y when x > 0.


when x = 0, the value of y is -2 * 0 = 0.


but y can't be equal to 0 because x can't be equal to 0.


when x > 0, the value of y = -2x.


x will always be negative and can never be equal to 0 because x can never be equal to 0.


the range is therefore all real values of y such that y < 0.


if you graph these equations, they will look like this.


<img src = "http://theo.x10hosting.com/2018/092802.jpg" alt="$$$" >


the open circle means the line goes up to but does not include that point.


the closed circle means the line goes up and and includes that point.