Graphs of Two Functions Find all values of x for which the graph of f lies above the graph of g.

step 1 We want to find every value of x where F of X, the graph of F of X, is above the graph of G of X

Graphs of Two Functions Find all values of x for which the...

Key Concepts

Graphing Functions

Graphing functions involves plotting the outputs of mathematical functions on a coordinate plane to visualize their behavior. This includes understanding how functions increase, decrease, and intersect, which is essential for comparing their relative positions.

Linear Functions

Linear functions are mathematical functions with a constant rate of change, typically represented by a straight line on a graph. They are fundamental in mathematics due to their simplicity and role as a baseline for comparing more complex functions.

Rational Functions

Rational functions are expressed as the ratio of two polynomials and often exhibit features like vertical and horizontal asymptotes. Their distinct behavior, especially near points of discontinuity, makes them a critical study topic in graph analysis.

Inequalities Involving Functions

Solving inequalities involving functions entails determining the intervals over which one function's values are greater than another's. This process often involves finding intersection points and testing the resulting intervals to see where the inequality holds.

Intersection Points

Intersection points are the values at which the output of two functions are equal. Identifying these points is crucial because they serve as boundaries that partition the domain into intervals for further analysis of the functions’ relative positions.

Domain Considerations

Domain considerations are essential when comparing functions because they define the set of input values for which each function is valid. Special attention must be paid to functions with restrictions, such as those involving division by zero, to avoid invalid solutions.

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