Graphing a Piecewise Function with Discontinuities

Math Problem Statement

Diberikan fungsi y sebagai berikut: y = -2, jika x ≤ 0; y = 3x, jika x > 0. Gambarlah grafik dari fungsi y tersebut.

The problem is asking to graph the given piecewise function $y$ , defined as:

\begin{cases} -2, & \text{if } x \leq 0 \\ 3x, & \text{if } x > 0 \end{cases}$$ Here’s how the graph can be sketched: ### Step-by-Step Guide: 1. **For $$x \leq 0$$:** - The function $$y = -2$$ is a horizontal line because $$y$$ is constant regardless of the value of $$x$$. This line exists for all $$x$$ less than or equal to 0. - At $$x = 0$$, $$y = -2$$ (closed dot). 2. **For $$x > 0$$:** - The function $$y = 3x$$ is a straight line with a slope of 3 and passes through the origin. - This part of the graph starts at $$x = 0$$, but since $$x = 0$$ belongs to the first case ($$y = -2$$), the point $$(0, 0)$$ is an open dot here. ### Graph Characteristics: - There is a discontinuity (a jump) at $$x = 0$$, transitioning from $$y = -2$$ to $$y = 3x$$. - For $$x > 0$$, the line grows rapidly as $$y$$ increases with a slope of 3. I can create a plot for you. Let me know if you’d like to see the graph! Would you like to proceed?

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Piecewise Functions
Graphing Linear Equations
Discontinuities

y = 3x

Grades 9-12

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