Questions: Sketch a graph of f(x) where f(x) = x+3

Transcript text: Sketch a graph of $f(x)$ where $f(x)=|x+3|$

Solution

Solution Steps

Step 1: Identify the Function

The given function is $ f(x) = |x + 3| $. This is an absolute value function, which means it will create a V-shaped graph.

Step 2: Determine the Vertex

The vertex of the absolute value function $ f(x) = |x + 3| $ occurs where the expression inside the absolute value is zero. Set $ x + 3 = 0 $ to find the vertex: \[ x = -3 \] So, the vertex is at the point $(-3, 0)$.

Step 3: Plot Key Points

To sketch the graph, plot the vertex and a few additional points on either side of the vertex:

For $ x = -4 $: \[ f(-4) = |-4 + 3| = |-1| = 1 \] Point: $(-4, 1)$
For $ x = -2 $: \[ f(-2) = |-2 + 3| = |1| = 1 \] Point: $(-2, 1)$
For $ x = -5 $: \[ f(-5) = |-5 + 3| = |-2| = 2 \] Point: $(-5, 2)$
For $ x = -1 $: \[ f(-1) = |-1 + 3| = |2| = 2 \] Point: $(-1, 2)$

Step 4: Draw the Graph

Using the vertex and the additional points, draw the V-shaped graph. The left side of the V will slope upwards from the vertex, and the right side will also slope upwards from the vertex.

Final Answer

The graph of $ f(x) = |x + 3| $ is a V-shaped graph with the vertex at $(-3, 0)$. The left arm of the V passes through points like $(-4, 1)$ and $(-5, 2)$, and the right arm passes through points like $(-2, 1)$ and $(-1, 2)$.

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