Instruction: All questions must be completed with full solutions and proper form to achieve full marks. 1. For the polynomial f (x) = -3x5 + 4x3 + 2x2 + 1 a) State the degree and the leading coefficient of [2 marks] Degree: _Leading Coefficient: b) Describe the end behaviour. Explain. [2 marks] c) State which finite differences will be constant. Explain. [1 mark] d) Determine the value of the constant finite differences. Show all work. [2 marks] 2. Determine the equation of the following polynomial. Show all the steps as shown in the examples. [5 marks] 3. Determine algebraically f(x) = -2x* + 3x2 + 7 is even or odd. Show work. [3 marks] 4. a) State whether f (x) = 3x5 - 2x3 + x is even, odd, or neither. Explain. [2 marks] b) State the type of symmetry of f (x) = 3x5 - 2x3 + x. Explain. [2 marks] 6. For the polynomial f (x) = 2(6 - 2x) (x + 1)?(x -2) a) State the Degree: and Leading coefficient: [2 marks] b) Describe the end behaviour. Explain [2 marks] c) State the x-intercepts and corresponding order. [3 marks] d) Find the y-intercept. Show work. [2 marks] e) Sketch the polynomial by hand. [2 marks] ) State the intervals where the function is positive and the intervals where it is negative. [2 marks] Interval Sign of f(x)