Question25 Graph $f(x)=|x+1|$ on the set of axes below.

Studdy Solution

STEP 1

1. We are graphing the function $f(x) = |x+1|$ .
2. The graph should be plotted on a set of axes.

STEP 2

1. Understand the behavior of the absolute value function.
2. Determine key points on the graph.
3. Plot the graph using the key points and the behavior of the function.

STEP 3

The function $f(x) = |x+1|$ is an absolute value function, which creates a V-shaped graph.
The vertex of the graph occurs where the expression inside the absolute value is zero. Solve $x + 1 = 0$ to find the vertex.

STEP 4

Solve for the vertex: $x + 1 = 0$ gives $x = -1$ .
The vertex is at the point $(-1, 0)$ .

STEP 5

Choose points to the left and right of the vertex to determine the shape of the graph.
For $x = -2$ , $f(-2) = |-2 + 1| = 1$ . The point is $(-2, 1)$ .
For $x = 0$ , $f(0) = |0 + 1| = 1$ . The point is $(0, 1)$ .

STEP 6

Plot the vertex $(-1, 0)$ and the points $(-2, 1)$ and $(0, 1)$ on the set of axes.
Draw lines connecting these points to form the V-shape of the absolute value graph.
The left arm of the V extends from $(-\infty, \infty)$ approaching the vertex from the left, and the right arm extends from the vertex to $(\infty, \infty)$ .
The graph of $f(x) = |x+1|$ is now plotted on the axes.

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