Math Problem Statement
Graph the following function on the axes provided: f(x) = {-5 for x ≤ 0; -2x + 8 for x ≥ 5}.
Solution
The function in the image is a piecewise function defined as follows:
\begin{cases} -5 & \text{for } x \leq 0 \\ -2x + 8 & \text{for } x \geq 5 \end{cases}$$ To graph this function, follow these steps: 1. **For $$x \leq 0$$**, the function is constant at $$f(x) = -5$$. This means that for any $$x \leq 0$$, the graph will be a horizontal line at $$y = -5$$ (from $$x = -\infty$$ to $$x = 0$$). 2. **For $$x \geq 5$$**, the function is $$f(x) = -2x + 8$$. This is a linear function with a slope of -2 and a y-intercept of 8. This means the graph will be a straight line starting from $$x = 5$$ and moving to the right. Now, you can plot these two segments: - A horizontal line at $$y = -5$$ for all $$x \leq 0$$. - A straight line starting at $$x = 5$$ for $$f(x) = -2x + 8$$. Would you like to know how to plot the function step by step on a graph, or do you have any other questions about this?Ask a new question for Free
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Math Problem Analysis
Mathematical Concepts
Piecewise Functions
Graphing Functions
Linear Equations
Formulas
Equation of a line: y = mx + b
Theorems
Definition of a piecewise function
Suitable Grade Level
Grades 9-12