Math Problem Statement

what is the definition of this function

What is the definition of this function?

Solution

This image shows a linear function graphed on a coordinate plane, with the points labeled at (−2,3)(-2,3), (0,0)(0,0), and (3,3)(3,3). From this, it seems to represent two line segments with differing slopes.

  1. Segment 1: Passes through (0,0)(0, 0) and (3,3)(3, 3), indicating a slope of 11 (since m=3−03−0=1m = \frac{3-0}{3-0} = 1).
  2. Segment 2: Connects (0,0)(0, 0) to (−2,3)(-2, 3), which has a negative slope. Calculating this slope: m=3−0−2−0=−32m = \frac{3 - 0}{-2 - 0} = -\frac{3}{2}

Thus, this represents a piecewise linear function:

-\frac{3}{2}x & \text{for } x \leq 0, \\ x & \text{for } x \geq 0. \end{cases}$$ Would you like further clarification, or have any specific questions about this? ### Related Questions 1. How do you find the slope of a line given two points? 2. What is a piecewise function, and how is it defined? 3. How can we determine the domain of a piecewise function? 4. How does the slope affect the direction of a line segment? 5. How would the graph look if the slopes were different? ### Tip When calculating slopes, remember the formula $$m = \frac{y_2 - y_1}{x_2 - x_1}$$ for two points $$(x_1, y_1)$$ and $$(x_2, y_2)$$.

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Math Problem Analysis

Mathematical Concepts

Algebra
Piecewise Functions
Slope Calculation

Formulas

Slope formula: m = (y2 - y1) / (x2 - x1)
Piecewise function notation

Theorems

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Suitable Grade Level

Grades 8-10

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