Here are the essential concepts you must grasp in order to answer the question correctly.
Inequalities
Inequalities are mathematical expressions that show the relationship between two values when they are not equal. They use symbols such as '≥' (greater than or equal to) and '≤' (less than or equal to) to indicate the range of possible solutions. Understanding how to interpret and graph inequalities is essential for visualizing the solutions on a coordinate plane.
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Logarithmic Functions
Logarithmic functions, such as log_2(x+1), are the inverses of exponential functions. They express the power to which a base must be raised to obtain a certain value. In this case, log_2(x+1) indicates the exponent to which 2 must be raised to yield (x+1). Familiarity with the properties and behavior of logarithmic functions is crucial for accurately graphing them.
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Graphs of Logarithmic Functions
Graphing Techniques
Graphing techniques involve plotting points and understanding the shape of functions on a coordinate plane. For inequalities, it is important to determine the boundary line (in this case, y = log_2(x+1)) and then shade the appropriate region that satisfies the inequality. Mastery of these techniques allows for effective visualization of solutions and their relationships.
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Graphs and Coordinates - Example