Graph each function. See Examples 1 and 2. h(x)=√(4x)

검증된 단계별 안내

Identify the function given: $h(x) = \sqrt{4x}$. This is a square root function where the expression inside the root is \$4x$.

Determine the domain of the function by setting the expression inside the square root greater than or equal to zero: $4x \geq 0$. Solve for $x$ to find the domain.

Create a table of values by choosing several $x$ values from the domain and calculating the corresponding $h(x)$ values using the formula $h(x) = \sqrt{4x}$.

Plot the points from the table on the coordinate plane, where the $x$-values are the inputs and the $h(x)$ values are the outputs.

Draw a smooth curve through the plotted points starting from the smallest $x$ in the domain, showing the shape of the square root function, which increases gradually as $x$ increases.

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주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

Square Root Function

A square root function involves the principal square root of an expression, such as h(x) = √(4x). It is defined only for values where the expression inside the root is non-negative, ensuring the output is a real number. Understanding its domain and range is essential for graphing.

Domain of a Function

The domain is the set of all input values (x-values) for which the function is defined. For h(x) = √(4x), the expression inside the root, 4x, must be greater than or equal to zero, so the domain is x ≥ 0. Identifying the domain helps determine where to plot the graph.

Graphing Transformations

Graphing transformations involve shifting, stretching, or compressing the basic graph of a function. Since h(x) = √(4x) can be seen as √(x) scaled horizontally by a factor of 1/4, understanding how multiplication inside the root affects the graph helps in sketching the correct shape.