# Given the function y={3x+1 if x=>0 or x-2 if x<0 Find its values for x=−1; 0; 1; 2.

###### Question:

Find its values for x=−1; 0; 1; 2.

## Answers

Answer:Step-by-step explanation:How can we solve equations such as the cubic equation shown here? x3 − x2 – 4x + 4 = 0There is an extremely complicated formula for solving cubic equations. Some calculators have this formula built in and therefore can be used to solve cubic equations.We are going to learn how these equations can be solved by factorising. If the equation has solutions that are integers a, b and c then we can factorise the equation as follows: x3 − x2 – 4x + 4 = (x − a)(x − b)(x − c) = 0Multiplying the brackets together we see that the constant term, 4, must be the number we get when we multiply a, b and c together. abc = 4All the solutions a, b and c must be factors of 4 so there are not many whole numbers that we need to consider.We have only the following possibilities: ±1, ±2 and ±4We’ll examine each of these numbers to find which ones are solutions of the equation. f(1) = 13 − 12 – 4×1 + 4 = 0 1 is a solution f(−1) = (−1)3 − (−1)2 – 4×(−1) + 4 = 6 f(2) = 23 − 22 – 4×2 + 4 = 0 2 is a solution f(−2) = (−2)3 − (−2)2 – 4×(−2) + 4 = 0 −2 is a solutionWe have now found three solutions so we don’t need to try 4 and −4 as a cubic equation has a maximum of three solutions.These three numbers give us the values of a, b and c and we can factorise the equation. x3 − x2 – 4x + 4 = (x − 1)(x − 2)(x + 2) = 0This method involves finding integers that are factors of ( can be divided into ) the constant term and then testing whether these integers are solutions of the equation.Unfortunately we cannot assume that the solutions of a third degree equation are all integers.However, if we can find one integer solution, lets say it is x = a then, by the remainder theorem , we know that (x − a) is a factor of the equation. We can find another factor, a quadratic factor, by division. We can then solve the quadratic equation by using the formula for solving quadratics. Example 1Solve the equation x3 − 3x2 – 2x + 4 = 0We put the numbers that are factors of 4 into the equation to see if any of them are correct. f(1) = 13 − 3×12 – 2×1 + 4 = 0 1 is a solution f(−1) = (−1)3 − 3×(−1)2 – 2×(−1) + 4 = 2 f(2) = 23 − 3×22 – 2×2 + 4 = −4 f(−2) = (−2)3 − 3×(−2)2 – 2×(−2) + 4 = −12 f(4) = 43 − 3×42 – 2×4 + 4 = 12 f(−4) = (−4)3 − 3×(−4)2 – 2×(−4) + 4 = −100The only integer solution is x = 1. When we have found one solution we don’t really need to test any other numbers because we can now solve the equation by dividing by (x − 1) and trying to solve the quadratic we get from the division. Now we can factorise our expression as follows: x3 − 3x2 – 2x + 4 = (x − 1)(x2 − 2x − 4) = 0It now remains for us to solve the quadratic equation. x2 − 2x − 4 = 0We use the formula for quadratics with a = 1, b = −2 and c = −4.We have now found all three solutions of the equation x3 − 3x2 – 2x + 4 = 0. They are: eftirfarandi: x = 1 x = 1 + Ö5 x = 1 − Ö5Example 2We can easily use the same method to solve a fourth degree equation or equations of a still higher degree. Solve the equation f(x) = x4 − x3 − 5x2 + 3x + 2 = 0.First we find the integer factors of the constant term, 2. The integer factors of 2 are ±1 and ±2. f(1) = 14 − 13 − 5×12 + 3×1 + 2 = 0 1 is a solution f(−1) = (−1)4 − (−1)3 − 5×(−1)2 + 3×(−1) + 2 = −4 f(2) = 24 − 23 − 5×22 + 3×2 + 2 = −4 f(−2) = (−2)4 − (−2)3 − 5×(−2)2 + 3×(−2) + 2 = 0 we have found a second solution.The two solutions we have found 1 and −2 mean that we can divide by x − 1 and x + 2 and there will be no remainder. We’ll do this in two steps.First divide by x + 2 Now divide the resulting cubic factor by x − 1. We have now factorisedf(x) = x4 − x3 − 5x2 + 3x + 2 intof(x) = (x + 2)(x − 1)(x2 − 2x − 1) and it only remains to solve the quadratic equation x2 − 2x − 1 = 0. We use the formula with a = 1, b = −2 and c = −1. Now we have found a total of four solutions. They are: x = 1 x = −2 x = 1 + x = 1 − hopefully this helps!:)

Answer: Which two equations represent the same function? A) y = 2x – 7 and f(x) = 7 – 2x B) 3x = y – 2 and f(x) = 3x – 2 C) f(x) = 3x2 + 5 and y = 3x2 + 5 D) None of the above Show/Hide Answer A) y = 2x – 7 and f(x) = 7 – 2x Incorrect. These equations look similar but are not the same. The first has a slope of 2 and a y-intercept of −7. The second function has a slope of −2 and a y-intercept of 7. It slopes in the opposite direction. They do not produce the same graph, so they are not the same function. The correct answer is f(x) = 3x2 + 5 and y = 3x2 + 5. B) 3x = y – 2 and f(x) = 3x – 2 Incorrect. These equations represent two different functions. If you rewrite the first equation in terms of y, you’ll find the equation of the function is y = 3x + 2. The correct answer is f(x) = 3x2 + 5 and y = 3x2 + 5. C) f(x) = 3x2 + 5 and y = 3x2 + 5 Correct. The expressions that follow f(x) = and y = are the same, so these are two different ways to write the same function: f(x) = 3x2 + 5 and y = 3x2 + 5. D) None of the above Incorrect. Look at the expressions that follow f(x) = and y =. If the expressions are the same, then the equations represent the same exact function. The correct answer is f(x) = 3x2 + 5 and y = 3x2 +Step-by-step explanation: