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: Plug the result back into the original equation to ensure it works. Problem 15.42: Range of a Function Finding the maximum or minimum value of on a specific interval Identify Monotonicity : The function is always increasing for Calculate Endpoints : State the Range : The values of fall between these two results. Problem 15.43: Intersection of Graphs Finding where the graph of intersects another line, such as Set Equations Equal : Write
: This typically results in a quadratic equation ( Solve the Quadratic : Find the possible values using the discriminant or factoring. : Plug the result back into the original
: Look for numbers that are perfect squares (e.g., Apply Root Properties : Use the property : Look for numbers that are perfect squares (e
Below are the step-by-step solutions for these problems, which typically cover the properties of and square functions ( ) in 8th-grade curriculum. Problem 15.39: Simplification of Radical Expressions : Plug the result back into the original
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: Perform addition or subtraction of the resulting rational numbers. Example : If the problem is , the result is Problem 15.40: Comparing Values