In this section, we will investigate methods for determining the domain and range of functions such as these.įigure 1 Based on data compiled by 3 Finding the Domain of a Function Defined by an Equation In creating various functions using the data, we can identify different independent and dependent variables, and we can analyze the data and the functions to determine the domain and range. Notice that we can use the data to create a function of the amount each movie earned or the total ticket sales for all horror movies by year. Figure 1 shows the amount, in dollars, each of those movies grossed when they were released as well as the ticket sales for horror movies in general by year. Consider five major thriller/horror entries from the early 2000s- I am Legend, Hannibal, The Ring, The Grudge, and The Conjuring. When big-budget actors, shooting locations, and special effects are included, however, studios count on even more viewership to be successful. Horror and thriller movies are both popular and, very often, extremely profitable. Find the domain of a function defined by an equation.So negative 2 is less than orĮqual to x, which is less than or equal to 5. So on and so forth,īetween these integers. In between negative 2 and 5, I can look at this graph to see Negative 2 is less than orĮqual to x, which is less than or equal to 5. What is its domain? So once again, this function It never gets above 8, but itĭoes equal 8 right over here when x is equal to 7. Value or the highest value that f of x obtains in thisįunction definition is 8. Or the lowest possible value of f of x that we get What is its range? So now, we're notįunction is defined. Is less than or equal to 7, the function isĭefined for any x that satisfies this double Here, negative 1 is less than or equal to x Way up to x equals 7, including x equals 7. So it's defined for negativeġ is less than or equal to x. This function is not definedįor x is negative 9, negative 8, all the way down or all the way What is its domain? Well, exact similar argument. Is less than or equal to x, which is less thanĬondition right over here, the function is defined. So the domain of thisĭefined for any x that is greater than orĮqual to negative 6. Wherever you are, to find out what the value of It only starts getting definedĪt x equals negative 6. It's not defined for xĮquals negative 9 or x equals negative 8 and 1/2 or Is equal to negative 9? Well, we go up here. We say, well, what does f of x equal when x ![]() Is the entire function definition for f of x. Right over here, we could assume that this What is its domain? So the way it's graphed ![]() One more point (0,6) would give 6>3 which is a true statement, and shading should include this point. If point is (1,5) you can do the same thing, 5 > 5, but this would be right on the line, so the line would have to be dashed because this statement is not true either. ![]() If you try points such as (0,0) and substitute in for x and y, you get 0 > 3 which is a false statement, and if you did it right, shading would not go through this point. So lets say you have an equation y > 2x + 3 and you have graphed it and shaded. The has to do with the shading of the graph, if it is >, shading is above the line, and ). Without the "equal" part of the inequality, the line or curve does not count, so we draw it as a dashed line rather than a solid line The "equal" part of the inequalities matches the line or curve of the function, so it would be solid just as if the inequality were not there.
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