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Ch. 2 - Graphs and Functions
Lial - College Algebra 13th Edition
Lial13th EditionCollege AlgebraISBN: 9780136881063Not the one you use?Change textbook
All textbooksLial 13th EditionCh. 2 - Graphs and FunctionsProblem 31
Chapter 3, Problem 31

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

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1
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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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

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.
Recommended video:
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Imaginary Roots with the Square Root Property

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.
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Domain Restrictions of Composed Functions

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.
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Intro to Transformations
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