create and sketch a factored rational function f(x) using the smallest possible exponents while having the following characteristics: 1. has restrictions at x=-2even, x=4odd, and x=-5hole 2. the end behavior of the graph levels off at y=-2 3. has zeroes at x=2odd, x=-3even, and x=0odd

6. Select the correct graph below of the function: (x) = x*(x + 2)(x – 2). List the x-intercepts. For each, state its multiplicity and why each either crosses the x- axis or simply touches the x-axis in terms of its multiplicity being odd or even. This problem is worth 8 points with 4 points for the graph selection and 4 points for the explanation of the intercepts.

Consider f (x) = 2x* – x3 – 5x2 + 2x + 2. 1. List all possible zeros (candidates) for f(x). 2. Define f (x) in your calculator or desmos. Use the graph to narrow down your candidates. Use synthetic division to reduce f (x) to a quadratic expression. Factor the resulting quadratic expression to find the last two zeros. ZEROS: 3. Express f(x) as a product of linear factors. Don't forget to include the value of a!

3. For the function f(x) = 2x4 – 5x3 + 9x² + x – 15: a. State the degree of the polynomial b. State the number of zeros the polynomial function will have. c. Use the Rational Zero Theorem to find all of the possible rational zeros d. Look at the graph or Table on a graphing calculator to determine which numbers on the list of rational zeros are real zeros indicated by the x-intercepts of the graph. In the space below, use synthetic division to verify one rational zero. Note: If the division remainder is zero, the number divided is a zero of the function. е. f. Find all remaining zeros. (Show work!) Note: Use the reduced polynomial (the quotient from the division) to continue the search for zeros © If the degree of the reduced polynomial is higher than 2, continue the synthetic division process with another real zero. (Remember: a number may be a multiple zero – i.e. occur more than once ) © Whenever the reduced polynomial is quadratic, the zeros can be found by using methods for…

Sketch the following functions by factoring first to determine intercepts, holes and asymptotes. Show all your work. 3. y = (x-2)(x²-4x+4) x²-4x-5