Evaluating Piecewise Functions Maze Answer Key (2024)

FAQs

How do I evaluate piecewise functions? ›

The first step in evaluating a piecewise function is to determine which function definition applies depending on the value of x that is being input. Once that has been determined, we evaluate the function as usual by substituting in the given value of x.

To graph piecewise functions, first identify where the domain is partitioned by boundary values. Graph functions on the domain using tools such as plotting points or transformations. Be sure to use open or closed circles on the endpoints of each domain based on whether the endpoint is included.

Summary. A piecewise function is a function where more than one formula is used to define the output over different pieces of the domain. Evaluating a piecewise function means you need to pay close attention to the correct expression used for the given input.

1.07 Piecewise functions | Grades 9-12 Math | Common Core Precalculus - 2020 Edition | Mathspace.

To find the zeros of a function graphically, simply list the 𝑥-coordinates of the points where a graph touches or crosses the 𝑥-axis. If those 𝑥-coordinates are not exact integer values, you will need to find the zeros algebraically.

With the unit step function, we can solve initial-value problems that involve piecewise-continuous functions. Solve y ″ + 9 y = 1 , 0 ≤ t < π 0 , t ≥ π subject to y(0) = y′(0) = 0. f ( t ) = 1 U ( t − 0 ) − U ( t − π ) + 0 U ( t − π ) = U ( t ) − U ( t − π ) .

A step function (or staircase function) is a piecewise function containing all constant "pieces". The constant pieces are observed across the adjacent intervals of the function, as they change value from one interval to the next. A step function is discontinuous (not continuous).

To find the domain of a piecewise function, first look at the domains of each function independently. Then check to see if any undefined areas are inside the restraints of the piecewise function. Then check for any other undefined areas. If no undefined areas are there, then the domain is all real x-values.

How to find domain and range? ›

To find the domain and range of an equation y = f(x), determine the values of the independent variable x for which the function is defined. To calculate the range of the function, we simply express the equation as x = g(y) and then find the domain of g(y).

Evaluating Piecewise Function

To evaluate a piecewise function at any given input, first, see which of the given intervals (or inequalities) the given input belongs to. Then just substitute the given input in the function definition corresponding to that particular interval.

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.

Tax brackets are another real-world example of piecewise functions. For example, consider a simple tax system in which incomes up to $10,000 are taxed at 10%, and any additional income is taxed at 20%. The tax on a total income, S, would be 0.1S if S≤ $10,000 and 1000 + 0.2 (S – $10,000), if S> $10,000.

In order to find limits of piecewise function, we have to take one sided limits separately, as a piecewise function has different formulas or functions in different intervals. In this example, one sided (right hand limit) limit exists, because the value of right hand limit and the functional value is equal.

f(x) is an EVEN function if and only if f(x) = f(-x) for all x in the domain of x. f(x) is an ODD function if and only if f(x) = -f(-x) for all x in the domain of x. else, f(x) is neither ODD nor EVEN. Here f(-x) = (-x)3 + 1 = - x3 + 1.