Explain, using the theorems, why the function is continuous at every number in its domain. F(x) = 2x²-x-3 +9 O F(x) is a polynomial, so it is continuous at every number in its domain. O F(x) is a rational function, so it is continuous at every number in its domain. O F(x) is a composition of functions that are continuous for all real numbers, so it is continuous at every number in its domain. O F(x) is not continuous at every number in its domain. none of these State the domain. (Enter your answer using interval notation.)

Are all polynomials rational functions? Are all algebraic functions polynomials?

Find the domain of the function: f(x) O All Real Numbers O {x\ x=4} Ο Ο Ο O {x|x = 4, x= 3} O (X1X=3) 3} x2 - 5x+6 x² - 7x+12

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!