Answer:
g(x) = |x+3|-2
Step-by-step explanation:
to move horizontally replace each x with (x ± c)
if you move it to the right, you need x - c
if you move it to the left , you need x + c
so , since we are moving 3 units to the left, we replace the x with x+3
g(x) = |x+3|-2
It is critical to open a compass with over half the way in order for the arcs formed to meet for perpendicular bisector.
<h3>What is perpendicular bisector?</h3>
A perpendicular bisector would be a line that cuts a line segment in half and forms a 90-degree angle at the intersection point. In other words, a perpendicular bisector separates a line segment now at midpoint, forming a 90-degree angle.
Now, consider an example;
When you wish to build a perpendicular line on a line segment, like line AB, you do the following;
- Set the compass on a radius more than half the length of the line AB.
- Using A as your center, draw an arc above and below line AB.
- With the same radius and B as our center, draw additional arcs on top or below line AB to join a first arcs on the both side of the line.
- Join the two arc intersections to cut line AB at M.
A line AB appears to be bisected perpendicularly as a result. The arcs would not have met if the compass is opened less than half way down line AB.
To know more about perpendicular bisector, here
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For finding the values, we look at the x - value given. Then we move to where it is on the graph and find its y value.
In part A, when x = -4, the y value looks to be between -3 and -4. Let's put it in the middle and estimate it at -3.5
In part B, when x = 1, the process is similar. Go to x = 1, then go to the graph, then go to the y value. That looks to be at y = -3.
In part C, when x = 4, there are three values that work. We are actually answering part D at this point because we can tell this graph is NOT a function of x. When you have an x -value that goes into the function, you have to get EXACTLY ONE thing that comes out. I bolded "EXACTLY ONE" because those words make the definition work. Two or more, not a function. One, it's a function. None, and it's not in the domain at all. There are three values of y that work, and they are - from top down, 3.5, 0, -2.5.
We answered Part D when observing part C. It's NOT a function because there is not EXACTLY ONE value of y for an x.
And finally, because it's not a function - finding the domain and range is a waste of time. You can't find the domain of something that's not a function - you need a function to have a domain.
Hope that helps.
