Math Mill

I used this as a homework assignment after introducing graphing rational expressions by noting their roots, holes, vertical asymptotes and domain from standard form by factoring. That's why there are detailed notes of how each factor matches to a feature of the graph.

This is a test review of all things logs. Use the entire review or just bits and pieces. Topics include evaluating logs, estimating logs, log properties, log equations and writing equations of functions from graphs (linear, quadratic, exponential and logarithmic).

This is a practice worksheet for finding all the features of a rational expression then graphing it. Then students find the features from the graph of a rational expression and with the expression in factored and standard forms. Features are: roots, y-intercepts, holes, domain, asymptotes (vertical, horizontal or slant/oblique)

This is an introduction to polynomial roots (real and complex) and using synthetic division. Students are given a polynomial and one factor then they must find the other factors and the roots. Then students are given graphs of polynomials and they must write the polynomial in factored and standard forms.

This worksheet allows students to practice naming types of functions, finding factors, roots, y-intercept, domain, range and end behavior from the function and graph. Then from the graph, students write the polynomial in factored and standard forms.

Students are given an equation or a graph and must find the factors, roots/zeros/x-intercepts/solutions, y-intercept, domain, range and end behavior. Then from the graphs, they write the function in factored and standard forms.

This is a practice worksheet for finding all the features of a rational expression then graphing it. Then students find the features from the graph of a rational expression and with the expression in factored and standard forms. Features are: roots, y-intercepts, holes, domain, asymptotes (vertical, horizontal or slant/oblique)

This is a worksheet for students to practice graphing rational expression by finding their y-intercepts, horizontal or slant (oblique) asymptotes based on whether the rational was proper or improper. They also use a graphing calculator for graphing then add the noted features. It's a nice application of polynomial division and graphing lines.

This is a review for a polynomial quiz. It is a hodge podge of items - polynomial and function types, degree, end behavior, factoring to solve quadratics, rational exponents, operations, writing functions from transformations.

I used this as and Exit Slip to assess my students on graphing rational expression by finding their y-intercepts, horizontal or slant (oblique) asymptotes based on whether the rational was proper or improper. The students had to add those features to the given graph. It's a nice application of polynomial division and graphing lines. There are 4 versions to keep the students from copying their neighbor.

These practice worksheets (Exit Slips) have students writing polynomials in factored and standard forms from root coordinates and graphs. Also noting domain and range, and end behavior from graphs. There are 4 versions to keep students from copying off their neighbor.

I used this as an Exit Slip for students to find all the roots (real, complex and/or radical) for polynomials. Then I gave them the roots and they had to write the polynomial in factored and standard forms. There are 4 different versions to make sure students don't copy their neighbor's paper.

This is a worksheet with some polynomial division problems. Some can be done with long division only or with long division or synthetic division. I used this as a classroom activity to practice division while teaching the students about finding slant/oblique asymptotes of rational expressions.

I used this as an Exit Slip to assess my students on graphing rational expressions by noting their roots, holes, vertical asymptotes and domain from standard to factored form. Students also look at graphs, pick out those key features and write the expression in factored and standard forms. There are 4 versions of the exit slip to keep students from copying off their neighbor.

The night before a quiz I always give a Last Practice for homework then send the students the answers - how do you study math, you do math. This is the Last Practice for graphing rational expressions by noting their roots, holes, vertical asymptotes and domain from standard to form.

This is a practice worksheet on graphing rational expression by finding their y-intercepts, horizontal or slant (oblique) asymptotes based on whether the rational was proper or improper. It's a nice application of polynomial division.

I used this as a Notes sheet when teaching my students about the y-intercept and horizontal or slant/oblique asymptotes of rational expressions based on whether the expression was proper or improper. I use synthetic and long division with the rationals. After each example, the students would graph the rational on their graphing calculators to see the y-intercepts and asymptotes.

I used this as my lesson examples when teaching my students how to graph rational expressions by noting their roots, holes, vertical asymptotes and domain from standard from by factoring.

I used this as my lesson and examples to teach about polynomials and their degrees/roots/factors while reviewing end behavior, y-intercepts and domain & range. All roots are real.

This is a last practice for a polynomial test. I give out last practices for homework the night before a test or quiz. Items consist of function type, operations (add, subtract, multiply and divide), writing polynomials given roots and lead coefficient, finding roots of polynomials. Given a graph, finding factors, standard form, end behavior, domain and range.