Math Problem Statement
Gráfica esa función a trozos
Solution
The given function is defined as a piecewise function:
\begin{cases} x - 3 & \text{si } x < 0 \\ x^2 + 3 & \text{si } 0 \leq x < 2 \\ \sqrt{x - 2} & \text{si } x \geq 2 \end{cases}$$ ### Let's break this down and then graph it step by step: 1. **For $$x < 0$$:** The function is $$g(x) = x - 3$$. - This is a linear function with a slope of 1 and a y-intercept of -3. - It will be a straight line passing through points like (-1, -4) and (-2, -5). 2. **For $$0 \leq x < 2$$:** The function is $$g(x) = x^2 + 3$$. - This is a quadratic function that opens upwards with its vertex at $$(0, 3)$$. - It will cover values from $$x = 0$$ to $$x = 2$$ and include points like $$(0, 3)$$ and $$(1, 4)$$. 3. **For $$x \geq 2$$:** The function is $$g(x) = \sqrt{x - 2}$$. - This is a square root function that starts at $$x = 2$$ with $$g(2) = 0$$ and increases as $$x$$ increases. - Points like $$(2, 0)$$, $$(3, 1)$$, and $$(4, 2)$$ are on this curve. ### **Graph of the Function:** Now, I'll plot the graph for you and analyze the domain and range.Ask a new question for Free
By Image
Drop file here or Click Here to upload
Math Problem Analysis
Mathematical Concepts
Piecewise Functions
Linear Functions
Quadratic Functions
Square Root Functions
Graphing Functions
Formulas
-
Theorems
-
Suitable Grade Level
High School