Here are the essential concepts you must grasp in order to answer the question correctly.
Square Root Function
The square root function, denoted as √x, is a fundamental mathematical function that returns the non-negative value whose square equals x. It is defined for all non-negative real numbers and has a characteristic 'half-parabola' shape when graphed. Understanding this function is crucial for analyzing the behavior of h(x) = √(4x), particularly its domain and range.
Recommended video:
Imaginary Roots with the Square Root Property
Transformation of Functions
Transformation of functions involves altering the graph of a parent function through shifts, stretches, or reflections. In the case of h(x) = √(4x), the factor of 4 indicates a vertical stretch of the square root function. Recognizing how these transformations affect the graph is essential for accurately plotting the function.
Recommended video:
Domain & Range of Transformed Functions
Domain and Range
The domain of a function refers to the set of all possible input values (x-values) for which the function is defined, while the range is the set of all possible output values (y-values). For h(x) = √(4x), the domain is x ≥ 0, since the square root is only defined for non-negative inputs, and the range is also y ≥ 0, as square roots yield non-negative outputs. Understanding these concepts is vital for graphing the function correctly.
Recommended video:
Domain & Range of Transformed Functions