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- 2. Let g(x) = f(x) u(x) where f is the quadratic function from problem 1 and u is the unit step function: u( x ) = 1 if x 20 0 if x<0 VA 1 y = u(x) (a) Write a piecewise formula for the function g. (b) Sketch a graph of y = g(x). (c) Indicate the domain and range of the function g. XTo find a quadratic function y=px^2+qx+r that best approximates this data, where xx is the input and yy is the output, we can minimize |Ax-b|, where Input 2 4 5 8 9 Output 30 2 -30 -102 -130 Find what A = and find what B =Find General solution to the following problem
- 1.Discuss two practical applications in which “piecewise functions” are used either explicitly or implicitly 2.To the best of your ability, using mathematical notion or in words, create any one of the functions you have spoken of in part (1) above. 3.If you could only learn one approach to solving quadratic equations, discuss which of the approaches you would choose and why? 4.Do you wholly agree with the statement that “the domain and range of a quadratic equation will be [-∞, ∞]”? Provide arguments to support your position.Show that the graph of f(x)=(3-4x)/e^2x has minimum value at x=5/4.QUESTION 7 Given the quadratic function f(x) = 2x2 + 6x + 5. a) Express in the form f(x) = a(x + p)2 + q with a, p and q is a constant. b) Hence, state the minimum value of f(x) and the corresponding value of x. c) The graph f(x) = 2x2 - mx + 2 cuts at the x - axis at two points. Find the range of values of m.
- If the function h(x)=(x-5)^5 is expressed in the form f o g with f(x)=x^5, then find the function g(x). Is this a decomposition problem? Why is the solution (x-5)^5? How can g(x)=h(x)? Thank you for the helpb and c are constants in this problemIf L(x)=mx+b is the linearization of the cube root of 3x+1 at x=333 , then b=. Enter your answer as a decimal. Use L(x) to approximate the cube root of 1003, the answer is . Enter your answer as a decimal.