Find the domain and sketch the graph of the function. f(x)= x+2 if x ⩽-1 x^2 if x>

step 1 This question asks us to find the domain and then sketch the graph of the function. What we know

Find the domain and sketch the graph of the function. f(x)=...

Key Concepts

Graphing Functions

Graphing a function involves plotting its points on a coordinate system and connecting them in a way that represents the function's behavior. This requires understanding the nature of the function's formula, identifying key points, intercepts, and overall trends, and ensuring that each piece of a piecewise function is accurately represented.

Continuity and Boundary Behavior

When dealing with functions that are defined by different expressions over different intervals, it is important to analyze the behavior at the boundaries where the definitions change. This involves checking whether the function is continuous at these partition points, which may include evaluating limits from each side to determine if the function connects smoothly or includes any jump discontinuities.

Piecewise-Defined Functions

This concept refers to functions that are defined by different expressions over different intervals of the independent variable. Each piece of the function has its own formula, and understanding how and when to apply each rule based on the input value is essential for analyzing the overall behavior of the function.

Domain of a Function

The domain of a function is the complete set of input values (typically x-values) for which the function is defined. Determining the domain involves identifying any restrictions on the inputs, such as values that could result in division by zero or negative values under an even root.

Transcript

Please give Ace some feedback