Answer:
Plot points: {(-2, 4), (-1, 3), (0, 2), (1, 1), (2, 0), (3, -1)}
Step-by-step explanation:
The vertex form of the absolute value function is: f(x)= a|x – h| + k
where:
(h, k) = vertex
a = determines whether the graph opens up or down.
h = determines how far left or right the parent function is translated.
- If h is positive, the function is translated h units to the right.
- If h is negative, the function is translated |h| units to the left.
k = determines how far up or down the parent function is translated.
- If k is positive, the function is translated k units up.
- If k is negative, the function is translated |k| units down.
Now that I've defined the variables in the function, using the given equation as a reference: f(x) = |x - 3| - 1, it means that the vertex occurs at (3, -1). And since a = 1, then it means that the graph opens upward. Now, we can start plotting points on the graph. Just like plotting other equations, you could practically choose any x-value, and substitute as the input for the function. Keep doing so until you plot enough points on the graph. As mentioned earlier, you already have the value for the vertex (3, -1) as the minimum point on the graph.
f(x) = |x - 3| - 1
if x = 0:
f(0) = |0 - 3| - 1
f(0) = |- 3| - 1
f(0) = 3 - 1
f(0) = 2
if x = 1:
f( 1 ) = |1 - 3| - 1
f( 1 ) = |- 2| - 1
f( 1 ) = 2 - 1
f( 1 ) = 1
if x = 2:
f(2) = |2 - 3| - 1
f(2) = |- 1| - 1
f(2) = 1 - 1
f(2) = 0
If x = -1:
f( -1 ) = |-1 - 3| - 1
f( -1 ) = |- 4| - 1
f( -1 ) = 4 - 1
f( -1 ) = 3
If x = -2
f(2) = |-2 - 3| - 1
f(2) = |- 5| - 1
f(2) = 5 - 1
f(2) = 4
All you need to do is plot the following points on the graph, since I've already done all the solution for you.
{(-2, 4), (-1, 3), (0, 2), (1, 1), (2, 0), (3, -1)}
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