In the function f(x) = |x|, what is the nature of the graph?

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Question: In the function f(x) = |x|, what is the nature of the graph?

Options:

Correct Answer: It is a V-shape.

Solution:

The graph of f(x) = |x| forms a V-shape, reflecting the absolute value function.

In the function f(x) = |x|, what is the nature of the graph?

In the function f(x) = |x|, what is the nature of the graph?

Step 1: Understand what the function f(x) = |x| means. The absolute value function takes any number x and makes it positive. For example, |3| = 3 and |-3| = 3.
Step 2: Identify the key points of the graph. The graph will have a point at (0, 0) because |0| = 0. It will also have points like (1, 1) and (-1, 1) because |1| = 1 and |-1| = 1.
Step 3: Plot the points on a graph. Start at (0, 0), then plot (1, 1) and (-1, 1).
Step 4: Connect the points. Draw straight lines from (0, 0) to (1, 1) and from (0, 0) to (-1, 1).
Step 5: Observe the shape. The lines create a V-shape, which is the graph of the function f(x) = |x|.

Absolute Value Function – The absolute value function outputs the non-negative value of its input, resulting in a V-shaped graph.