Unit 3 relations and functions homework 4 function notation and ...

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Unit 3 relations and functions homework 4 function notation and evaluating functions answer key

In mathematics, a function is a rule that take an input value (often \(x\)) and assigns it an output value (often \(y\)). What makes a function special is that for any given input, there is only one output. Function notation, which is used in all of mathematics, is a way of writing out the rule that relates the input and output values of a function. In this lesson, we will look at how function notation works, how to evaluate a function given the function notation, and how to evaluate a function from its graph. Table of Contents Reading function notation Function notation is written using the name of the function and the value you want to find the output for. For example, \(f(x)\) is read "\(f\) of \(x\)" and means "the output of the function \(f\) when the input is \(x\)". Another example is something like \(g(2)\). This is read "\(g\) of 2" and represents the output of the function \(g\) for the input value of 2. To help you understand this notation, let's look at a couple of examples. Example When \(x = 2\), the value of a function \(y = f(x)\) is 10. Use function notation to represent this. Solution The function is written as \(f(x)\). This means that the input of the function is \(x\). Since \(x = 2\), we can start by writing: \(f(2)\) The example says that when \(x = 2\), the output is 10. Since the notation \(f(2)\) represents the output for the input of 2, we can write this as: \(\bbox[border: 1px solid black; padding: 2px]{f(2) = 10}\) Evaluating functions using function notation When it comes to evaluating functions, you are most often given a rule for the output. To evaluate the function means to use this rule to find the output for a given input. You can do this algebraically by substituting in the value of the input (usually \(x\)). This is shown in the next couple of examples. Example For \(f(x) = 2x + 1\), find \(f(3)\). Solution Start with your function. \(f(x) = 2x + 1\) Let \(x = 3\) and then calculate the value of the function. To do this, replace each \(x\) in the rule with 3. \(f(3) = 2(3) + 1\) Simplify to find the final answer. \(\begin{align}&= 6 + 1\\ &= \bbox[border: 1px solid black; padding: 2px;]{7}\end{align}\) When evaluating a function, make sure that you replace every \(x\) in the rule with the input value. Pay close attention, because there may be more than one \(x\) to replace. Example For \(f(x) = 3x^2 ? 5x + 1\), find \(f(?2)\). Start with your function. \(f(x) = 3x^2 ? 5x + 1\) Let \(x = ?2\) by replacing each \(x\) in the rule with ?2 and then simplify to find your final answer. \(\begin{align}f(-2) &= 3(-2)^2 ? 5(-2) + 1 \\ &= 3(4) + 10 + 1\\ &= 12 + 10 + 1 \\ &= \bbox[border: 1px solid black; padding: 2px;]{23}\end{align}\) It is also possible to evaluate a function using an input that is an algebraic expression. This is more complicated since you usually will need simplify your answer, but it still follows the same idea of substitution. Example Let \(f(x) = ?3x + 7\). Find and simplify \(f(m + 1)\), where \(m\) is a real number. Solution Start with your function. \(f(x) = -3x + 7\) Just as you did with numbers, let \(x = m + 1\) and evaluate the function. This means replace every \(x\) in the rule with "\(m + 1\)". \(f(m+1) = -3(m+1) + 7\) Apply the distributive property by multiplying ?3 and each term within the parentheses. The combine like terms to simplify. \(\begin{align}&= -3m-3 + 7\\ &= \bbox[border: 1px solid black; padding: 2px;]{-3m+4}\end{align}\) From here, you can get much more complicated with things like the difference quotient, which is used later in calculus. Even with these more complicated examples, you will still apply the same concept we did to each of the examples above. Evaluating functions using a graph The graph of a function is a way of viewing the outputs of the function for all possible inputs. Here, we let \(y = f(x)\) so that each y-value represents the output and each x-value represents the input. This means any point on the graph is: \((x, y) = (\text{input}, \text{corresponding output})\) Remember that in the xy-plane, the x-axis is the horizontal axis, and the y-axis is the vertical axis. Using this, we can easily read points off the graph. You can do this for the graph of just about any function. For example, if we wanted to know the value of \(f\) when \(x = -1\) for the function below, we would just find \(x = -1\) on the x-axis and use the graph to find the corresponding yvalue. There are some types of functions, where you have to be a little more careful. Piecewise defined functions and functions with asymptotes often have more going on in the graph. However, those are studied later on in algebra. For now, you should make sure you can read the graphs of functions like those shown in the examples above. Summary Functions are used in all parts of mathematics, and understanding function notation is necessary for a wide variety of problems. Remember that it is simply a way of relating the input of a function to the value of its output. The notation \(f(x)\) is always read "\ (f\) of \(x\)" though the function may have a different name like \(g\) or \(k\) (then we could write \(g(x)\) for "\(g\) of \(x\)" or \(k(x)\) for "\(k\) of \(x\)"). Bringing you closer to the people and things you love. -- Instagram from FacebookConnect with friends, share what you're up to, or see what's new from others all over the world. Explore our community where you can feel free to be yourself and share everything from your daily moments to life's highlights.Express Yourself and Connect With Friends* Add photos and videos to your INSTA story that disappear after 24 hours, and bring them to life with fun creative tools.* Message your friends in Direct. Start fun conversations about what you see on Feed and Stories.* Post photos and videos to your feed that you want to show on your profile.Learn More About Your Interests* Check out IGTV for longer videos from your favorite INSTA creators.* Get inspired by photos and videos from new INSTA accounts in Explore.* Discover brands and small businesses, and shop products that are relevant to your personal style.Parental Guidance RecommendedUsers Interact, Shares Info, Shares LocationRUB 85.00 - RUB 459.00 per item A 11 day CCSS-Aligned Functions Unit - including identifying, comparing, and analyzing functions, evaluating using function notation, reading graphs using function notation, and writing equations for real life applications.Standards: 8.F.1, 8.F.2, 8.F.3, 8.F.4, 8.F.5Unit overview: This unit bundle contains , standards, student objective, notes, warm-up, homework assignments, two quizzes, review activities, and a unit test that cover the following topics:Day 11. Identify parts of the graph --------------------------------------------Activity 1: Understanding the coordinate plane (notes)Activity 6: Extra practice 2. Create graph from real life data ---------------------------------------Activity 2: Bubble contestActivity 3: Average temperature 3. Interpret graph from real life data -------------------------------------Activity 4: Jayla's distance from homeActivity 5: Rocket launch (HOMEWORK)Day 21. Understanding function notation -------------------------------------------Activity 1: Understanding the function notation (notes)2. Use function notation to interpret real life data --------------------Activity 2: Temperature in Central ParkActivity 3: Acceleration and deceleration of a sports carActivity 4: Water tank volumeActivity 5: Temperature during the week (HOMEWORK)Day 3QUIZ - Assessment V1 on Day 1-2 QUIZ - Assessment V2 on Day 1-2 Day 41. Write order pair using function notation -------------------------------Activity 1: Understanding the function notationActivity 2: Function notation from tablesActivity 3: Function notation from graphActivity 4: Writing coordinate points as function notationDay 51. Define a function and identify the domain and range -----------------Activity 1: The Redbox as a function machineNotes on functionActivity 2: Relation or function Activity 3: Creating examples of functions and relations Activity 4: Redbox machine Do Now or Exit ticket Thinglink Activity (HOMEWORK)Day 61. Use vertical line test to determine function -------------------------Do NowActivity 1: Investigating vertical line testActivity 2: function or not using the vertical line testActivity 3: function or not using the vertical line test Activity 4: Possible or not (HOMEWORK)Day 7QUIZ - Assessment V1 on Day 4-5 QUIZ - Assessment V2 on Day 4-5 Extra practice (HOMEWORK)Day 81. Evaluate functions using the function notation ----------------------Do Now Activity 1: Equation notation vs function notation (notes)Activity 2: Equation notation vs function notation Guided notes on evaluatingActivity 3: Evaluating functions given inputActivity 4: Evaluating functions given outputActivity 5: Why is sand called sand ? Evaluating Riddle (HOMEWORK)Day 91. Use function notation in context -------------------Do Now Activity 1: Season pass to six flagsActivity 2: Renting a carActivity 3: Greeting cardsActivity 4: Cellphone billActivity 5: Draining the pool (HOMEWORK)Day 10 1. Review the function unit Activity 1: Scavenger hunt on evaluating functions Activity 2: Draining the pool Activity 3: Function or notActivity 4: Amount of coffee in a cup Day 11Unit Exam Displaying top 8 worksheets found for - Gina Wilson Unit 3 Home Work Answer Keys.Some of the worksheets for this concept are Unit 5 homework 2 gina wilson 2012 answer key, Unit 3 relations and functions, Gina wilson all things algebra 2012 answers ebook, Gina wilson all things algebra 2013 answers, Geometry unit 3 homework answer key, 12 3 inscribed angles work answers, 12 3 inscribed angles work answers, Unit 9 study guide answer key.Found worksheet you are looking for? To download/print, click on pop-out icon or print icon to worksheet to print or download. Worksheet will open in a new window. You can & download or print using the browser document reader options.

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