Will f(x) +4 have real zeros? Justify without any

Will f(x) +4 have real zeros? Justify without any calculations.

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MATH 107 Coursework Assignment: Show Work for All Problems

INSTRUCTIONS:

SHOW WORK FOR ALL PROBLEMS

 

  1. Consider the quadratic equations:

 

Solve quadratic equation above by

  1. extracting square roots
  2. completing the square
  3. by applying the formula

 

  1. Consider the function:

 

  1. Will f(x) +4 have real zeros? Justify without any calculations.
  2. Will f(x) -5 have real zeros? Justify without any calculations.
  3. Will f(x-2) have real zeros? Justify without any calculations.
  4. Will f(x+4) have real zeros? Justify without any calculations.

 

  1. Consider the function
    1. Determine the behaviors as   and as
    2. Find all zeros. What is the multiplicity of roots (zeros)?
    3. When will the function cross the x-axis? When will it cross the y-axis?

 

  1. Consider the function 
    1. Find the domain for the function in interval notations
    2. Find all vertical, horizontal and slant asymptotes
    3. Sketch the function
    4. Solve the inequality 
CONTENT:

SHOW WORK FOR ALL PROBLEMS 1 Consider the quadratic equations: x2-2=0 Solve quadratic equation above by * extracting square roots X2-2=0 X2=2 X= = ± √2= {-1.4142, 1.4142} * completing the square Reordering the terms: -2 + X2 = 0 Move all terms containing X to the left, all other terms to the right. -2 + 2 + X2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + X2 = 0 + 2 X2 = 0 + 2 Combine like terms: 0 + 2 = 2 X2 = 2 Taking the square root of each

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