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. Step 1: The graph of the function ƒ(x)=|x| is a V-shaped graph. This is because the absolute value function always returns a non-negative value. When x is positive, the value of |x| is x itself. When x is negative, the value of |x| is -x, which is a positive number. Therefore, the graph of ƒ(x)=|x| is symmetric with respect to the y-axis and opens upwards.
2. Step 2: To find the function value when x=1.5, substitute x=1.5 into the function ƒ(x)=|x|. Since 1.5 is a positive number, the absolute value of 1.5 is 1.5 itself.
3. Step 3: Therefore, the function value when x=1.5 is 1.5.

Key Concepts

Absolute Value Function

The absolute value function, denoted as ƒ(x) = |x|, outputs the non-negative value of x regardless of its sign. This means that for any input x, the function returns x if x is positive or zero, and -x if x is negative. The graph of this function is a V-shape, with the vertex at the origin (0,0) and symmetric about the y-axis.

Graphing Functions

Graphing functions involves plotting points on a coordinate plane to visually represent the relationship between the input (x) and output (ƒ(x)). For the absolute value function, the graph consists of two linear segments that meet at the origin, illustrating how the function behaves differently for positive and negative values of x.

Function Evaluation

Function evaluation is the process of finding the output value of a function for a specific input. For the function ƒ(x) = |x|, to evaluate it at x = 1.5, you substitute 1.5 into the function, resulting in ƒ(1.5) = |1.5| = 1.5. This demonstrates how to compute the function's value based on the defined rule.