To answer each question, refer to the following basic graphs. Which one is the graph of ƒ(x)=|x|? What is the function value when x=1.5?

Verified step by step guidance

1. Recall that the function ƒ(x) = |x| represents the absolute value of x, which means it outputs the distance of x from zero on the number line, always as a non-negative value.
2. The graph of ƒ(x) = |x| is a V-shaped graph that touches the origin (0,0) and opens upwards, with two linear pieces: one with a positive slope for x ≥ 0 and one with a negative slope for x < 0.
3. Identify the graph among the given options that has this V shape, with the vertex at the origin and symmetric arms extending upwards on both sides.
4. To find the function value when x = 1.5, substitute 1.5 into the function: ƒ(1.5) = |1.5|.
5. Since the absolute value of a positive number is the number itself, the function value at x = 1.5 is simply 1.5.

Key Concepts

Absolute Value Function

The absolute value function, denoted as ƒ(x) = |x|, outputs the non-negative value of x. It transforms any negative input into its positive counterpart, making the graph V-shaped with a vertex at the origin (0,0). Understanding this function is essential to identify its graph and evaluate its values.

Graph Interpretation

Graph interpretation involves recognizing the shape and key features of a function's graph. For ƒ(x) = |x|, the graph consists of two linear pieces: one with positive slope for x ≥ 0 and one with negative slope for x < 0. Identifying these characteristics helps in matching the function to its graph.

Function Evaluation

Function evaluation means substituting a specific input value into the function to find the corresponding output. For ƒ(x) = |x|, evaluating at x = 1.5 involves calculating the absolute value of 1.5, which is 1.5. This process confirms the function's value at a given point.