Domain #x^24x21# is a polynomial I don't need to worry about dividing by zero or taking even roots or negative numbers or other weirdness The domain is all real numbers (The interval #(oo, oo)# Range This may depend on ow much you know I would graph (or at least think about the graph) of the parabola whose equation id #y=x^24x21#What is the domain?Get an answer for 'Find the domain and range of the following y = x^2 , y = sqrt(1 – x^2), y = 1/x, y = sqrt(x) , y = sqrt(4x) ' and find homework help for other Math questions at eNotes
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Y=x^2-4x+1 domain and range-Math\begin{align}f(x)&=x^2–4x7\\&=(x2)^23\end{align}\tag*{}/math Range of this function is mathy\ge 3/math for domain mathx\in\R/math Suppose thatName_____ ID 1 Date_____ Period____ ©x z2o0Y1t6s _KJuUtXaD KSgoefutZwOayreet SLuLKCVi N JAhl`lm SrqizgLhJtsG gr^esAeDrjvRe^dk1State whether each function is linear, quadratic, or exponential Identify the domain and range 1) y = 2x2 4x 1 x y 1 2 2) 3x 5y = 0 x y
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I have a function here y = x^2 4x 32 I have some questions about it 1Domain/Range Domain xvalues (inputs) Range yvalues (outputs) The domain of quadratics will always be "all real numbers" (doesn't matter if max or min) Two ways to write the domain and range Algebra 1 Domain all real numbers Range y > # (if minimum) y < # (if maximum)Alternative method Write f ( x) as x − 1 ( x − 1) 2 2 Thus, your function is a horizontal shift of g ( t) = t t 2 2, and hence these functions have the same range Next, g is odd, so it is sufficient to study positive t (for which g is positive) Now, by the arithmeticgeometric mean t 2 2 ≥ 2 t 2 2 = 2 2 t with equality when t 2 = 2
Find the domain, range, and axis of symmetry a) y = x 2 2x 3 b) y = x 2 4x 1 47 Quadratic Formula If ax 2 bx c = 0 and a=0 then 2a Ex 1 Use the quadratic formula to solve the equationsAll equations of the form a x 2 b x c = 0 can be solved using the quadratic formula 2 a − b ± b 2 − 4 a c The quadratic formula gives two solutions, one when ± is addition and one when it is subtraction x^ {2}4xy6=0 − x 2 4 x − y − 6 = 0 This equation is in standard form ax^ {2}bxc=0 Substitute 1 for a, 4 for b The range is much harder You could complete the square to get the range, which I will do after we get the answer The simplest way to get the smallest part of the range is to graph the quadratic The lowest point is at (2, 25) so the range is Range25 ≤ y < ∞ Completing the square y = x^2 4x 21 y = (x^2 4x) 21
Question What are the vertex, axis of symmetry, maximum or minimum value, domain and range for Y=x^24x3 Answer by TimothyLamb(4379) (Show Source) You can put this solution on YOUR website!x^2 4x 3the above quadratic equation is in standard form, with a=1 to obtain vertex form use completing the square ∙ coefficient of the x2 term must be 1 which it is ∙ add/subtract (1 2 coefficient of xterm)2 to x2 −4x ⇒ y = x2 2( − 2)x4−4 7 ⇒ y = (x −2)2 3 ⇒ vertex = (2,3) and a > 0 ⇒ range is y ∈ R,y ≥ 3 graph {x^24x7 10, 10,Page 13 ____ 3 If an object is dropped from a height of 39 feet, the function h(t)= −16t 2 39 gives the height of the object after t seconds Graph the function A C B D ____ 4 Find the equation of the axis of symmetry and the coordinates of the vertex of the graph of y= 4x 2 5x−1
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≤ 2 The summary of domain and range is the following Example 4 Find the domain and range of the quadratic function y = {x^2} 4x 1 Just like our previous examples, a quadratic function will always have a domain of all x values I want to go over this particular example because the minimum or maximum is not quite obviousDivide 4, the coefficient of the x term, by 2 to get 2 Then add the square of 2 to both sides of the equation This step makes the left hand side of the equation a perfect square Square 2 Add y1 to 4 Factor x^ {2}4x4 In general, when x^ {2}bxc is a perfect square, it can always be factored as \left (x\frac {b} {2}\right)^ {2} Homework Statement For the following questions, find the Domain and Range Use either the graph or turning point method Homework Equations 1 y= x6x8 2 y= x^23x5 3 y= x^24x4 And a question on the matter, when you complete the square, as in when I
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Get an answer for 'find the requested values a) f(x)=x^24x1 standard form, vertex, xintercept, yintercept, domain, range,' and find homework help for other Math questions at eNotesSolve your math problems using our free math solver with stepbystep solutions Our math solver supports basic math, prealgebra, algebra, trigonometry, calculus and more Can you identify the domain and range of the functions y=x²2x3 and y=x² 4x 1 1 See answer eyrah eyrah Domain of both are All Real numbers (infinity, infinity) Range of y=x^22x3 is 4, infinity) Range of y = x^24x1 (infinity, 3 New questions in Math I Make a table of values for each equation that defines a linearfunction
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Divide 4 by 1 x^ {2}4x=y Divide y by 1 x^ {2}4x\left (2\right)^ {2}=y\left (2\right)^ {2} Divide 4, the coefficient of the x term, by 2 to get 2 Then add the square of 2 to both sides of the equation This step makes the left hand side of the equation a In this case, we are only looking at a portion of the function, so our domain of values would be {1, 2, 3, and 4} and our range of values would be {7, 11, 15, and 19} Let's try a couple of examples What is the domain and range of the function \(y=x^{2}4x3\)?Given the equation {eq}\displaystyle y=3x^{2}12x7 {/eq}, graph the equation and find the domain, range, and line of symmetry Parabolas The graph of a quadratic function will be a parabola
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Solve your math problems using our free math solver with stepbystep solutions Our math solver supports basic math, prealgebra, algebra, trigonometry, calculus and moreChapter 5 Functions Learners must be able to determine the equation of a function from a given graph Discuss and explain the characteristics of functions domain, range, intercepts with the axes, maximum and minimum values, symmetry, etcAn increasing linear function with independent variable x and dependent variable y approaches the point (−1, 1) If this function is defined only when x is greater than −1 and y is greater than 1, what are the domain and range of this function?(1 Algebra Hiya!
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Free functions domain calculator find functions domain stepbystep This website uses cookies to ensure you get the best experience By using this website, you agree to our Cookie Policy Arithmetic Mean Geometric Mean Quadratic Mean Median Mode Order Minimum Maximum Probability MidRange Range Standard Deviation Variance Lower Quartile Since x^2 is always positive, the parabola grows upward if the coefficient is positive, and downward if it is negative The easy way to find the vertex and axis is to complete the square y = x^2 4x 32 = x^24x4 28 = (x2)^2 28 So the vertex is at (2,28) the axis is x=2 Naturally, the minimum is at the vertex 28Question 862 Graph and answer the questions f(x) = x^2 4x 1 What are the coordinates of the vertex?
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Find the Domain and Range y=4x y = 4x y = 4 x The domain of the expression is all real numbers except where the expression is undefined In this case, there is no real number that makes the expression undefined Interval Notation (−∞,∞) ( ∞, ∞) Set Builder Notation {xx ∈ R} { x x ∈ ℝ } The range is the set of all validFind the Domain and Range x^2y^2=4 x2 y2 = 4 x 2 y 2 = 4 Subtract x2 x 2 from both sides of the equation y2 = 4−x2 y 2 = 4 x 2 Take the square root of both sides of the equation to eliminate the exponent on the left side y = ±√4− x2 y = ± 4 x 2 Example \(\PageIndex{4}\) Finding the Domain and Range of a Quadratic Function Find the domain and range of \(f(x)=−5x^29x−1\) Solution As with any quadratic function, the domain is all real numbers Because \(a\) is negative, the parabola opens downward and has a maximum value We need to determine the maximum value
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The domain of a function is the set of all input values that you're "legally" allowed to plug into the function For the function y = x − 2, that's going to be x ≥ 2 because if you were to plug in, say, 1, you would end up with a negative number under the square root and, as you probably know, the square root function is not defined forWhat is the range? Find the domain and range of y = − x2 4x − 3 My Attempt y = f(x) = − x2 4x − 3 The given function is a polynomial of degree 2 in x f(x) is defined for all x ∈ R, so the domain of f = R Again, y = − x2 4x − 3 y = − (x2 − 4x 3) y = − (x − 1)(x − 3) y = (x 1)(x − 3) functions Share asked Nov 18 '17 at 227
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Answer and Explanation 1 For the function y = −x2−4x−7 y = − x 2 − 4 x − 7 , x x is the independent variable whereas y y is the dependent variable The function does not haveGraph the quadratic function f(x)=x^22x3Find its Vertex Form ( completing the square)Find the x and y interceptsFind the axis of symmetryFind its domain aFind the Domain and Range y=x^26x5 The domain of the expression is all real numbers except where the expression is undefined In this case, there is no real number that makes the expression undefined Interval Notation SetBuilder Notation The range is the set of all valid values
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Get stepbystep solutions from expert tutors as fast as 1530 minutes Your first 5 questions are on us!Algebra Find the Domain and Range f (x)=x^24x3 f (x) = x2 − 4x 3 f ( x) = x 2 4 x 3 The domain of the expression is all real numbers except where the expression is undefined In this case, there is no real number that makes the expression undefined Interval NotationFind the Domain and Range y=x^24 y = x2 − 4 y = x 2 4 The domain of the expression is all real numbers except where the expression is undefined In this case, there is no real number that makes the expression undefined Interval Notation (−∞,∞) ( ∞, ∞) Set Builder Notation {xx ∈ R} { x x ∈ ℝ } The range is the set
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The range is simply y ≤ 2 The summary of domain and range is the following Example 4 Find the domain and range of the quadratic function y = x 2 4 x − 1 y = {x^2} 4x 1 y = x2 4x − 1 Just like our previous examples, a quadratic function will always have a domain of all x values Domain is the limits of x Since this is a polynomial without any x's in the denominator, it is continuous from ∞ to ∞, that is, Domain is all real values of x Range is the limits of y Easiest way to find this, if your instructor allows it, isG (x) = x 2 4x Range of a Function For every value given to the independent variable from the domain in a function, we get a corresponding y value The set of all such y values is called the range of the function Example h (x) = 1/ (x 1)/ (x 3) The Domain is (∞, 1) ∪ (1
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Get an answer for 'Given the function 'f(x)=x^24x1' find the inverse of the function f, stating its domain A break down of how the answer is got would be much apprecitatedthanks in advanceThe domain is the list of numbers that can be plugged in for x
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