x - intercept : None
Y- intercept: (0, -5)
Step-by-step explanation
X-intercept is the point on f(x) where the value of y=0.
Given the function f(x) = -2| x+1 | - 3
To find the x - intercept, put f(x) = 0 and solve for x.
0 = -2| x + 1 | - 3
Add 3 to both-side of the equation.
3 = -2 | x + 1 |
Divide both-side of the equation by -2.
- 1.5 =| x + 1|
|x + 1 | = - 1.5
There is no value of x that satisfies the above equation.
Hence, there is no x - intercepts.
Y- intercept
It is a point on the function f(x) at which x = 0.
To find the y-intercept, substitute x = 0 into the equation given and simplify.
f(0) = -2|0+1| - 3
f(0) = -2|1| - 3
f(0) = - 2 - 3
f(0) = -5
Hence, the y-intercept is (0, -5)