The y-intercept is (0, -4) and x-intercept is (4/3, 0).
Given,
f(x)=|3x+1|-5
We need to find the x and y-intercept.
What are the x-intercept and y-intercept?
The point at which the given function passes through the x-axis is called the x-intercept and the point at which the given function passes through the y-axis is called the y-intercept.
For x-intercept we use y = 0.
For y-intercept we use x = 0.
We have,
f(x)=|3x+1|-5
Consider y = f(x)
Putting x = 0
we have,
y = |3x0 + 1| - 5
= |1| - 5
= 1 - 5 = -4
The y-intercept is (0, -4).
Putting y = 0
We have,
0 = |3x + 1| - 5
0 = 3x + 1 - 5
0 = 3x - 4
Adding 4 on both sides.
4 = 3x - 4 + 4
4 = 3x
x = 4/3
The x-intercept is (4/3, 0)
Thus the y-intercept is (0, -4) and x-intercept is (4/3, 0).
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