Though students often find function questions intimidating, solving a function is not dissimilar to solving simple equations (mathematical expressions in one variable set equal to a constant, for example, 2x + 5 = 15). The main difference is that when solving a function, rather than searching for a single solution (e.g., x = 5 in the above example), students must determine the function's domain and range. To work successfully with functions in algebra, students should know a few basic facts about them.
The domain of a function is the set of input values, or x-values, for that function. These values, together, comprise the independent variable.
The range of a function is the set of output values, or y-values, the function will give you when each value in the domain is input into the function. These, together, comprise the dependent variable.
To determine whether an equation is a function, look at a variety of coordinate points (x,y) or the graph of that equation. If the equation is indeed a function, each of the x-values will have only one y-value associated with it. Therefore, an equation that produces the coordinate points (1,2) and (1,3) is not a function.
To solve a function for its y-value at a given point, simply plug in a number, or x-value. Therefore, if you have the equation f(x) = 2x + 1, and you want to know what the value of that function is at x=3, plug in 3 to get f(3) = 2(3) + 1, or 7.
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