When Posting Here In The Weekly Summary Section Please Do No

Question

Whenposting Here In The Weekly Summary Section Please Do Not Post An When posting here in the Weekly Summary section, students are instructed not to simply provide answers but to demonstrate their problem-solving process step-by-step. Showing these steps is beneficial for learning, especially when answers are incorrect, as it allows identification of mistakes and collaborative correction. Correct solutions are important and should be accompanied by detailed explanations to ensure clarity and understanding. Specific problems to be solved include evaluating functions at given points, determining the domain of rational functions, deriving lines from given points, writing lines in slope-intercept form, solving equations, and using formulas such as the quadratic formula. In each case, students must clearly show their work, including formulas used, calculations, and reasoning, rather than just the final answer.

Dr. Jack HW Helper · Accepted Answer

In this paper, I will demonstrate how to approach and solve each of the provided mathematical problems step by step, ensuring that the methodology is transparent and educational. Problem 1: Evaluate f(-1) for f(x) = 4x² - 3x + 2 Given the function f(x) = 4x² - 3x + 2, we are asked to evaluate f(-1). This means substituting x = -1 into the function: f(-1) = 4(-1)² - 3(-1) + 2 Calculate each term: (-1)² = 1, so 4 * 1 = 4 -3 * (-1) = +3 Now sum these with 2: f(-1) = 4 + 3 + 2 = 9 Problem 2: State the domain of f(x) = (x + 3) / (x - 1) This is a rational function. The only restriction for the domain is where the denominator equals zero, since division by zero is undefined: x - 1 ≠ 0 → x ≠ 1 Therefore, the domain of f(x) is all real numbers except x = 1: Domain: {x ∈ ℝ | x ≠ 1} Problem 3: Write the equation of the line passing through (1, 1) and (2, 4) in slope-intercept form First, find the slope (m) using the two points: m = (y₂ - y₁) / (x₂ - x₁) = (4 - 1) / (2 - 1) = 3 / 1 = 3 Now, use point-slope form with point (1, 1): y - y₁ = m(x - x₁) y - 1 = 3(x - 1) Expand: y - 1 = 3x - 3 Finally, solve for y to get slope-intercept form: y = 3x - 3 + 1 = 3x - 2 Problem 4: Write the equation of a line with slope 2/3 and y-intercept 1 Using the slope-intercept form y = mx + b, where m = 2/3 and b = 1: y = (2/3)x + 1 Problem 5: Solve (4x + 1)(2x - 7) = 0 Set each factor equal to zero: 4x + 1 = 0 → 4x = -1 → x = -1/4 2x - 7 = 0 → 2x = 7 → x = 7/2 Solutions are x = -1/4 and x = 7/2. Problem 6: Evaluate f(x+h) for different functions Given f(x) = 4x + 3 f(x + h) = 4(x + h) + 3 = 4x + 4h + 3 Given g(x) = x² g(x + h) = (x + h)² = x² + 2xh + h² Given f(x) = -x + 1 f(x + h) = -(x + h) + 1 = -x - h + 1 Problem 7: Evaluate f(x - h) where f(x) = -x + 1 f(x - h) = -(x - h) + 1 = -x + h + 1 Problem 8: Use the quadratic formula to solve x² - x - 1 = 0 The quadratic formula is: x = [-b ± √(b² - 4ac)] / 2a Identify coefficients: a = 1, b = -1, c = -1 Compute the discriminant: Δ = b² - 4ac = (-1)

When Posting Here In The Weekly Summary Section Please Do No ✓ Solved

Whenposting Here In The Weekly Summary Section Please Do Not Post An

Sample Paper For Above instruction

Problem 1: Evaluate f(-1) for f(x) = 4x² - 3x + 2

Problem 2: State the domain of f(x) = (x + 3) / (x - 1)

Problem 3: Write the equation of the line passing through (1, 1) and (2, 4) in slope-intercept form

Problem 4: Write the equation of a line with slope 2/3 and y-intercept 1

Problem 5: Solve (4x + 1)(2x - 7) = 0

Problem 6: Evaluate f(x+h) for different functions

Given f(x) = 4x + 3

Given g(x) = x²

Given f(x) = -x + 1

Problem 7: Evaluate f(x - h) where f(x) = -x + 1

Problem 8: Use the quadratic formula to solve x² - x - 1 = 0

Conclusion

References