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When we have a function in formula form, it is usually a simple matter to evaluate the function. For example, the function [latex]f\left(x\right)=5 - 3{x}^{2}[/latex] can be evaluated by squaring the input value, multiplying by 3, and then subtracting the product from 5. How To: EVALUATE A FUNCTION Given ITS FORMula.
Example: Evaluating FunctionsGiven the function [latex]h\left(p\right)={p}^{2}+2p[/latex], evaluate [latex]h\left(4\right)[/latex]. In the following video we offer more examples of evaluating a function for specific x values. Example: Evaluating Functions at Specific ValuesFor the function, [latex]f\left(x\right)={x}^{2}+3x - 4[/latex], evaluate each of the following.
Try ItGiven the function [latex]g\left(m\right)=\sqrt{m - 4}[/latex], evaluate [latex]g\left(5\right)[/latex]. In the next video, we provide another example of how to solve for a function value. Example: Solving FunctionsGiven the function [latex]h\left(p\right)={p}^{2}+2p[/latex], solve for [latex]h\left(p\right)=3[/latex]. Try ItGiven the function [latex]g\left(m\right)=\sqrt{m - 4}[/latex], solve [latex]g\left(m\right)=2[/latex]. Evaluating Functions Expressed in FormulasSome functions are defined by mathematical rules or procedures expressed in equation form. If it is possible to express the function output with a formula involving the input quantity, then we can define a function in algebraic form. For example, the equation [latex]2n+6p=12[/latex] expresses a functional relationship between [latex]n[/latex] and [latex]p[/latex]. We can rewrite it to decide if [latex]p[/latex] is a function of [latex]n[/latex]. How To: Given a function in equation form, write its algebraic formula.
Example: Finding an Equation of a FunctionExpress the relationship [latex]2n+6p=12[/latex] as a function [latex]p=f\left(n\right)[/latex], if possible. Watch this video to see another example of how to express an equation as a function. Example: Expressing the Equation of a Circle as a FunctionDoes the equation [latex]{x}^{2}+{y}^{2}=1[/latex] represent a function with [latex]x[/latex] as input and [latex]y[/latex] as output? If so, express the relationship as a function [latex]y=f\left(x\right)[/latex]. Try ItIf [latex]x - 8{y}^{3}=0[/latex], express [latex]y[/latex] as a function of [latex]x[/latex]. Q & AAre there relationships expressed by an equation that do represent a function but which still cannot be represented by an algebraic formula? Yes, this can happen. For example, given the equation [latex]x=y+{2}^{y}[/latex], if we want to express [latex]y[/latex] as a function of [latex]x[/latex], there is no simple algebraic formula involving only [latex]x[/latex] that equals [latex]y[/latex]. However, each [latex]x[/latex] does determine a unique value for [latex]y[/latex], and there are mathematical procedures by which [latex]y[/latex] can be found to any desired accuracy. In this case, we say that the equation gives an implicit (implied) rule for [latex]y[/latex] as a function of [latex]x[/latex], even though the formula cannot be written explicitly. Evaluating a Function Given in Tabular FormAs we saw above, we can represent functions in tables. Conversely, we can use information in tables to write functions, and we can evaluate functions using the tables. For example, how well do our pets recall the fond memories we share with them? There is an urban legend that a goldfish has a memory of 3 seconds, but this is just a myth. Goldfish can remember up to 3 months, while the beta fish has a memory of up to 5 months. And while a puppy’s memory span is no longer than 30 seconds, the adult dog can remember for 5 minutes. This is meager compared to a cat, whose memory span lasts for 16 hours. The function that relates the type of pet to the duration of its memory span is more easily visualized with the use of a table. See the table below.
At times, evaluating a function in table form may be more useful than using equations. Here let us call the function [latex]P[/latex]. The domain of the function is the type of pet and the range is a real number representing the number of hours the pet’s memory span lasts. We can evaluate the function [latex]P[/latex] at the input value of “goldfish.” We would write [latex]P\left(\text{goldfish}\right)=2160[/latex]. Notice that, to evaluate the function in table form, we identify the input value and the corresponding output value from the pertinent row of the table. The tabular form for function [latex]P[/latex] seems ideally suited to this function, more so than writing it in paragraph or function form. How To: Given a function represented by a table, identify specific output and input values.
Example: Evaluating and Solving a Tabular FunctionUsing the table below,
Try ItUsing the table from the previous example, evaluate [latex]g\left(1\right)[/latex] . Finding Function Values from a GraphEvaluating a function using a graph also requires finding the corresponding output value for a given input value, only in this case, we find the output value by looking at the graph. Solving a function equation using a graph requires finding all instances of the given output value on the graph and observing the corresponding input value(s). Example: Reading Function Values from a GraphGiven the graph below,
Try ItUsing the graph, solve [latex]f\left(x\right)=1[/latex]. Try ItYou can use an online graphing tool to graph functions, find function values, and evaluate functions. Watch this short tutorial to learn how.
Contribute!Did you have an idea for improving this content? We’d love your input. Improve this pageLearn More How do you evaluate a function for the given value of x?Evaluating a function means finding the value of f(x) =… or y =… that corresponds to a given value of x. To do this, simply replace all the x variables with whatever x has been assigned. For example, if we are asked to evaluate f(4), then x has been assigned the value of 4.
How do you find a function on a calculator?How to Use a Function Calculator?. Step 1: Enter the function f(x) in the given input field.. Step 2: Click the button “Graph” to get the output.. Step 3: The graph of the function will be displayed in a new window.. Read: What is a Function?. f (x) = y.. Is Mathway a calculator?Mathway is a Web calculator that not only solves math problems for you, but also shows you how it got to the answer with step-by-step directions.
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