Calculate the coordinates of the points of intersection of the graph of y=|2x-3|-2 with the coordinates axes.
The answer shows that:
y=|2x-3|-2
When X=0, y=3-2=1
I don't get why it is 3, shldnt it be -3? And for modulus don't we have to do the positive and negative one when we take out the modulus?
Thks for yr help!
It is +3 because of he | | surrounding the 2x-3. the | | mean absolute, anything in between the | | will result in a positive number.
when x=0, y=abs(2*0-3) -2
but abs(-3)=3
To calculate the coordinates of the points of intersection, we need to find the values of x and y when the graph of the equation y = |2x - 3| - 2 intersects the coordinate axes.
Let's start with the x-axis, where y = 0. We can substitute y = 0 into the equation and solve for x:
0 = |2x - 3| - 2
To solve this equation, we need to consider two cases:
1. When 2x - 3 is positive:
If we assume 2x - 3 is positive, the equation becomes:
0 = (2x - 3) - 2
0 = 2x - 3 - 2
0 = 2x - 5
Solving for x:
2x = 5
x = 5/2
2. When 2x - 3 is negative:
If we assume 2x - 3 is negative, the equation becomes:
0 = -(2x - 3) - 2
0 = -2x + 3 - 2
0 = -2x + 1
Solving for x:
2x = 1
x = 1/2
So, there are two points of intersection on the x-axis: (5/2, 0) and (1/2, 0).
Now, let's move on to the y-axis, where x = 0. We can substitute x = 0 into the equation and solve for y:
y = |2(0) - 3| - 2
y = |-3| - 2
y = 3 - 2
y = 1
So, the point of intersection on the y-axis is (0, 1).
Regarding your confusion about the value of y when x = 0, you are correct that the modulus function can have both positive and negative values. However, in this specific equation, we are subtracting 2 from the absolute value of (2x - 3). As a result, the output of the modulus function will always be positive (or zero) minus 2. In the case when x = 0, 2x - 3 evaluates to -3, which is positive when put inside the modulus. Hence, we get y = |-3| - 2 = 3 - 2 = 1.
I hope this helps! Let me know if you have any further questions.