Math 107 Quiz 4 Name______________ 1. Consider the quadratic equations: 2 x 2=0 Solve quadratic equation above by a. extracting square roots b. completing the square c. by applying the formula 2. Consider the function: f ( x )=x 2 +4 a. b. c. d. Will f(x) +4 have real zeros? Justify without any calculations. Will f(x) -5 have real zeros? Justify without any calculations. Will f(x-2) have real zeros? Justify without any calculations. Will f(x+4) have real zeros? Justify without any calculations. 3. Consider the function f ( x )=x 5x 3 a. Determine the behaviors as x and as x b. Find all zeros. What is the multiplicity of roots (zeros)? c. When will the function cross the x-axis? When will it cross the y-axis? 2 4. Consider the function f ( x )= x 1 x3 a. Find the domain for the function in interval notations b. Find all vertical, horizontal and slant asymptotes c. Sketch the function d. Solve the inequality x 21 <1 x3