Math Problem Statement

Graph only

Graph the piecewise function: f(x) = { 2x if x < 0, -8x + 3 if x ≥ 0 }

Solution

The piecewise function provided in the image is:

\begin{cases} 2x & \text{if } x < 0 \\ -8x + 3 & \text{if } x \geq 0 \end{cases}$$ To graph this function: 1. **For $$x < 0$$:** The function is $$f(x) = 2x$$. This is a straight line with a slope of 2, passing through the origin (0,0). However, since this function is only valid for $$x < 0$$, we draw this line only for negative $$x$$-values. 2. **For $$x \geq 0$$:** The function is $$f(x) = -8x + 3$$. This is a straight line with a slope of -8 and a y-intercept of 3. This part is only valid for $$x \geq 0$$. Here is a breakdown of how the graph would look: - For $$x < 0$$, plot points for negative $$x$$-values (like $$x = -1, -2$$) and find the corresponding $$y$$-values using the equation $$2x$$. - For $$x \geq 0$$, plot points for non-negative $$x$$-values (like $$x = 0, 1$$) using the equation $$-8x + 3$$. - At $$x = 0$$, the value from $$-8x + 3$$ is $$3$$, so there is a point at $$(0, 3)$$. Would you like me to plot the graph for you, or do you want details on any specific aspect? Here are 5 related questions: 1. What happens if we modify the slopes in this piecewise function? 2. How do you find the slope of each part of a piecewise function graphically? 3. What is the domain and range of the given piecewise function? 4. How does the graph change if the conditions on $$x$$ are swapped? 5. How can you identify discontinuities in a piecewise function graph? **Tip:** When graphing piecewise functions, always check if the transition points are continuous or if there’s a jump (discontinuity).

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Math Problem Analysis

Mathematical Concepts

Piecewise Functions
Linear Equations
Graphing

Formulas

f(x) = 2x for x < 0
f(x) = -8x + 3 for x ≥ 0

Theorems

-

Suitable Grade Level

Grades 9-12

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