Math Problem Statement
How to graph each function
How to graph each function?
Solution
The image you uploaded shows a piecewise function , defined as follows:
\begin{cases} 3 & \text{if } x < -1 \\ x + 1 & \text{if } x > 1 \end{cases}$$ Here’s how to graph this piecewise function: 1. **First piece**: For $$x < -1$$, the function is constant and equals 3. This means you draw a horizontal line at $$y = 3$$ for all values of $$x$$ less than $$-1$$. However, the endpoint at $$x = -1$$ is **not included** (so the dot at $$x = -1, y = 3$$ should be open). 2. **Second piece**: For $$x > 1$$, the function is linear and follows $$y = x + 1$$. This is a straight line, where for each value of $$x$$, $$y$$ is one unit more than $$x$$. The point $$(1, 2)$$ is part of this line, but the endpoint at $$x = 1$$ is also **not included** (so the dot at $$x = 1, y = 2$$ should be open). ### Steps for graphing: 1. Start by plotting the points and lines based on the given intervals. 2. For the part $$x < -1$$, draw a horizontal line at $$y = 3$$ and ensure that the dot at $$(-1, 3)$$ is open. 3. For $$x > 1$$, plot a straight line with a slope of 1 starting from just past $$x = 1$$, and make sure the dot at $$(1, 2)$$ is also open. 4. Connect the pieces properly, with no connection between the segments at $$x = -1$$ and $$x = 1$$ because they are not defined at these points. Would you like a more detailed explanation of any specific step, or a visual representation of this graph? Let me know! Here are 5 related questions you might find useful: 1. How do you graph other piecewise functions? 2. How do you determine the domain and range of a piecewise function? 3. What are open and closed dots in piecewise functions? 4. How do you handle discontinuities in a graph? 5. Can piecewise functions have more than two pieces? Tip: Always ensure that you're clear on whether a point is included or excluded in the function's definition when graphing!Ask a new question for Free
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Math Problem Analysis
Mathematical Concepts
Piecewise Functions
Graphing Functions
Formulas
h(x) = 3 for x < -1
h(x) = x + 1 for x > 1
Theorems
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Suitable Grade Level
Grades 9-11