Math Problem Statement
f(x)={ −x+5 ∣x−4∣ for x<2 for x≥2
Solution
It seems like you're defining a piecewise function . Let's rewrite it clearly:
\begin{cases} -x + 5 & \text{for } x < 2 \\ x - 4 & \text{for } x \geq 2 \end{cases}$$ This means that the function behaves differently depending on the value of $$x$$: - **When $$x$$ is less than 2**: The function is defined as $$f(x) = -x + 5$$. - **When $$x$$ is greater than or equal to 2**: The function is defined as $$f(x) = x - 4$$. Would you like to see how to graph this function, find its domain and range, or any other details? Here are some follow-up questions you might find helpful: 1. What is the graph of this piecewise function? 2. How do you find the domain and range of the function? 3. What is the value of $$f(x)$$ at $$x = 2$$? 4. How does the function behave as $$x$$ approaches 2 from the left and right? 5. Can we find the points of intersection with the x-axis? **Tip:** When dealing with piecewise functions, carefully check the conditions for each piece to understand the overall behavior of the function.Ask a new question for Free
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Math Problem Analysis
Mathematical Concepts
Piecewise functions
Formulas
-
Theorems
-
Suitable Grade Level
High school
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