# 11 domain and range assignment answers

### Domain and Range

Intro to functions. Domain and range. Function notation. Linear vs Quadratic functions. Investigating the roles of a, h and k in the vertex form.

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Sketching quadratics functions in vertex form. Properties of a Parabola Assignment -found at the end of Day 6 handout. Changing from vertex form to standard expanded form.

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Completing the Square. Completing the Square:. Part 2. Word Problems Part 2. Word Problems Assignment. Test Review. Types of Factoring Note. Factoring: Special cases. Factoring Assignment. Quiz: Factoring. Graphs of quadratics in factored form :. Relating roots and zeros of quadratic functions. Graphing factored form notes. Nov Graphs of quadratics in factored form : Part 2. Converting between the three forms of a quadratic function. Quadratic formula. The Discriminant. Quiz: Quadratic formula.

Word Problems: Population growth, integers, geometric areas. Assessment and Evaluation. Wasylnka's Grade 11 Mixed Math. Search this site. Wasylnka's Classroom Home. Exponential Functions. Quadratic Functions.

December exam review. Homework Assignments. Contact Me.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. 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.

In this section, we will investigate methods for determining the domain and range of functions such as these. In Functions and Function Notation, we were introduced to the concepts of domain and range. In this section, we will practice determining domains and ranges for specific functions. Keep in mind that, in determining domains and ranges, we need to consider what is physically possible or meaningful in real-world examples, such as tickets sales and year in the horror movie example above.

We also need to consider what is mathematically permitted. For example, we cannot include any input value that leads us to take an even root of a negative number if the domain and range consist of real numbers. Or in a function expressed as a formula, we cannot include any input value in the domain that would lead us to divide by 0. We can write the domain and range in interval notationwhich uses values within brackets to describe a set of numbers. In interval notation, we use a square bracket [ when the set includes the endpoint and a parenthesis to indicate that the endpoint is either not included or the interval is unbounded.

We will discuss interval notation in greater detail later.

## Domain And Range Worksheet 2 Answers

Oftentimes, finding the domain of such functions involves remembering three different forms. First, if the function has no denominator or an even root, consider whether the domain could be all real numbers.

Third, if there is an even root, consider excluding values that would make the radicand negative. First identify the input values. The input value is the first coordinate in an ordered pair. There are no restrictions, as the ordered pairs are simply listed. The domain is the set of the first coordinates of the ordered pairs.

How To: Given a function written in equation form, find the domain.Here is a graphic preview for all of the Domain and Range Worksheets. You can select different variables to customize these Domain and Range Worksheets for your needs. The Domain and Range Worksheets are randomly created and will never repeat so you have an endless supply of quality Domain and Range Worksheets to use in the classroom or at home.

We have domain and range mapping diagrams, identifying functions from graphs, determining domains and ranges from graphs, and determining domains and ranges from ordered pairs. Our Domain and Range Worksheets are free to download, easy to use, and very flexible. These Domain and Range Worksheets are a good resource for students in the 9th Grade through the 12th Grade. Identifying Functions from Mapping Diagrams Worksheets These Algebra 1 Domain and Range Worksheets will produce problems for identifying whether mapping diagrams are functions or not.

You can select the types of values as well as the number of values in each mapping diagram. Identifying Functions from Ordered Pairs Worksheets These Algebra 1 Domain and Range Worksheets will produce problems for finding the domain and range of sets of ordered pairs.

You can select the range of numbers used in ordered pairs as well as whether the sheet should ask if each set of pairs is a function or not.

Identifying Functions from Graphs Worksheets These Algebra 1 Domain and Range Worksheets will produce problems for identifying whether graphed sets are functions or not.

You can select the types of functions and non-functions to be graphed. Identifying Domains and Ranges from Graphs Worksheets These Algebra 1 Domain and Range Worksheets will produce problems for finding the domain and range of graphed sets. You can select the types of things graphed as well as whether the sheet should ask if each graph is a function or not. Worksheets By Topics. Identifying Functions from Mapping Diagrams.

Identifying Functions from Ordered Pairs. Identifying Functions from Graphs. Identifying Domains and Ranges from Graphs.

All rights reserved.What is a domain? What is a range? Why are they important? How can we determine the domain and range for a given function?

### Algebra II : Domain and Range

It is the set of all values for which a function is mathematically defined. It is quite common for the domain to be the set of all real numbers since many mathematical functions can accept any input.

Domain and Range Word Problems

For example, many simplistic algebraic functions have domains that may seem… obvious. What values can we put in for the input x of this function? Well, anything! The answer is all real numbers.

Only when we get to certain types of algebraic expressions will we need to limit the domain. We can demonstrate the domain visually, as well. What values are valid inputs? Visually we see that as a line that extends forever in the x directions left and right.

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A straight, horizontal line, on the other hand, would be the clearest example of an unlimited domain of all real numbers. What would stop us, as algebra students, from inserting any value into the input of a function? We need a function that, for certain inputs, does not produce a valid outputi. Here is an example:. This function is defined for almost any real x. Division by zero is undefined. Therefore 1 is not in the domain of this function.

We cannot use 1 as an input, because it breaks the function. Makes sense, right? Look for places that could result in a division by zero condition, and write down the x-values that cause the denominator to be zero. Those are your values to exclude from the domain. Why does that cause issues with the domain?

Because, at least in the realm of real numbers, we cannot solve for the square root of a negative value. What values are excluded from the domain? Anything less than 2 results in a negative number inside the square root, which is a problem. Therefore the domain is all real numbers greater than or equal to 2. However, the most common example of a limited domain is probably the divide by zero issue. When asked to find the domain of a function, start with the easy stuff: first look for any values that cause you to divide by zero.

In that case, it would not be a valid input so the domain would not include such values. The range of a simple, linear function is almost always going to be all real numbers. A graph of a typical line, such as the one shown below, will extend forever in either y direction up or down. The range of a non-horizontal linear function is all real numbers no matter how flat the slope might look.

In that case, the range is just that one and only value.What are the domain and range of this function? A sine curve represent a wave the repeats at a regular frequency. The x-values span all real numbers, as there is no limit to the input fo a sine function.

The domain of the function is all real numbers and the range is. A function has to pass the vertical line test, which means that a vertical line can only cross the function one time. To put it another way, for any given value ofthere can only be one value of. For instance, ifthen. But ifas well. This function fails the vertical line test.

The other functions listed are a line,the top half of a right facing parabola,a cubic equation,and a semicircle. These will all pass the vertical line test.

The domain is the set of possible value for the variable. We can find the impossible values of by setting the denominator of the fractional function equal to zero, as this would yield an impossible equation.

Now we can solve for. There is no real value of that will fit this equation; any real value squared will be a positive number. The radicand is always positive, and is defined for all real values of. What is the domain of the function? This function is a parabola that has been shifted up five units. The standard parabola has a range that goes from 0 inclusive to positive infinity. If the vertex has been moved up by 5, this means that its minimum has been shifted up by five.

Based on the members of the function, the only limit that you have is the non-allowance of a negative number because of the square root. The square and the linear terms are fine with any numbers. You cannot have any negative values, otherwise the square root will not be a real number.Of which being said, we supply you with a assortment of simple yet beneficial content as well as templates designed well suited for virtually any academic purpose.

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## 1.3: Domain and Range

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