MAT-121: COLLEGE ALGEBRA
Written Assignment 4
2.5 points each
For the following exercise, rewrite the quadratic function in standard form and give the vertex.
For the following exercise, determine whether there is a minimum or maximum value to the quadratic function. Find the value and the axis of symmetry.
For the following exercise, rewrite the quadratic function in standard form and give the vertex. Determine whether there is a minimum or maximum value to the quadratic function. Find the value and the axis of symmetry. Determine the domain and range of the quadratic function.
For the following exercise, use the vertex (h, k) and a point on the graph (x, y) to find the general form of the equation of the quadratic function.
For the following exercise, identify the function as a power function, a polynomial function, or neither.
For the following exercise, find the degree and leading coefficient for the given function if it is a polynomial. If it is not a polynomial, then state so.
For the following exercise, find the intercepts of the functions.
For the following exercise, graph the polynomial function using a calculator or a graphing utility. Based on the graph, determine the intercepts and the end behavior.
For the following exercise, use the written statement to construct a polynomial function that represents the required information.
For the following exercise, find the x-intercept of the polynomial function. Express the intercept in point (ordered pair) form.
For the following exercise, use the Intermediate Value Theorem to confirm that the given polynomial has at least one zero within the given interval.
For the following exercise, graph the polynomial function. Note x- and y-intercepts, multiplicity, and end behavior.
For the following exercises, use the given information about the polynomial graph to write the equation.
For the following exercises, use long division to divide. Specify the quotient and the remainder.
For the following exercises, use synthetic division to find the quotient.
For the following exercises, use synthetic division to determine whether the first expression is a factor of the second. If it is, indicate the factorization.
For the following exercises, use synthetic division to find the quotient and remainder.
For the following exercises, use synthetic division to determine the quotient involving a complex number.
For the following exercises, use the Remainder Theorem to find the remainder which is the value of f(x) at x = k. Then evaluate f(x) at x = k to verify remainder and f(x) at x = k are the same. Show all work for both synthetic division and the evaluation of f(x) at x = k.
For the following exercises, use the Factor Theorem to find all real zeros for the given polynomial function and one factor.
For the following exercises, use the Rational Zero Theorem to find all real zeros. State all the possible rational zeros.
For the following exercises, find all complex solutions (real and non-real).
Use Descartes’ Rule to determine the possible number of positive and negative solutions. Make a table of possible real/complex solutions as shown in example 8 of Section 5.5. Then graph to confirm which of those possibilities is the actual combination.
For the following exercises, use your graphing calculator or a graphing utility program to graph the polynomial function. Based on the graph, find the rational zeros. All real solutions are rational.
For the following exercises, construct a polynomial function of least degree possible using the given information.
For the following exercises, find the dimensions of the right circular cylinder described.
For the following exercises, find the domain of the rational functions.
29.
For the following exercises, find the x- and y-intercepts for the functions.
30.
For the following exercises, find the slant asymptote of the functions.
31.
For the following exercises, find the horizontal intercepts, the vertical intercept, the vertical asymptotes, and the horizontal or slant asymptote of the functions. Use that information to sketch a graph.
For the following exercises, write an equation for a rational function with the given characteristics.
33. Vertical asymptotes at, x-intercepts at
, y-intercept at
, horizontal asymptote at
For the following exercises, find the inverse of the function on the given domain.
For the following exercises, find the inverse of the functions.
For the following exercises, find the inverse of the functions.
For the following exercises, find the inverse of the function and graph both the function and its inverse.
For the following exercises, write an equation describing the relationship of the given variables.
For the following exercises, write an equation describing the relationship of the given variables. Then use the given information to find the unknown value.
For the following exercises, use the given information to answer the questions.
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