For the given functions the intercepts are:
y-intercept (0, 6)
x-intercepts: (-2, 0) and (4, 0)
How to find the intercepts?
Here we have the function:
f(x)= -3*|x - 1| + 9
First, to find the y-intercept we need to evaluate in x = 0, then we will get:
f(0) = -3*|0 - 1| + 9
f(0) = -3*1 + 9 = 6
The y-intercept is 6.
To find the x-intercepts we need to find the values of x such that the function becomes zero.
0 = -3*|x - 1| + 9
-9/-3 = |x - 1|
3 = |x - 1|
We can break this into two equations:
-3 = x - 1
3 = x - 1
Solving the two equations we will get:
-3 + 1 = x
-2 = x
And:
3 = x - 1
3 + 1 = x
4 =x
These are the two x-intercepts.