Questions: Graph this function: y=x-1-4

Transcript text: Graph this function: \[ y=|x-1|-4 \]

Solution

Solution Steps

Step 1: Find the vertex

The given function is in the form $y = |x - h| + k$, where $(h, k)$ is the vertex. In our case, $y = |x - 1| - 4$. Thus, the vertex is $(1, -4)$.

Step 2: Find other points

We can find other points on the graph by choosing $x$ values and calculating the corresponding $y$ values. For $x = 0$, $y = |0 - 1| - 4 = |-1| - 4 = 1 - 4 = -3$, so we have the point $(0, -3)$. For $x = 2$, $y = |2 - 1| - 4 = |1| - 4 = 1 - 4 = -3$, so we have the point $(2, -3)$. For $x = -1$, $y = |-1 - 1| - 4 = |-2| - 4 = 2 - 4 = -2$, so we have the point $(-1, -2)$. For $x = 3$, $y = |3 - 1| - 4 = |2| - 4 = 2 - 4 = -2$, so we have the point $(3, -2)$.

Step 3: Plot and connect

Plot the vertex $(1, -4)$ and the points $(0,-3)$, $(2,-3)$, $(-1,-2)$, and $(3,-2)$. Connect the points to form a "V" shape, with the vertex at the bottom of the "V".

Final Answer:

The graph of $y = |x - 1| - 4$ is a V-shaped graph with the vertex at $(1, -4)$ and passing through the points $(0, -3)$, $(2, -3)$, $(-1, -2)$, and $(3, -2)$.

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