Week 16 – Solving Rational Equations

This week I learned how to solve rational equations.

Here is a common question:

This question asked me to solve the equation. The first step was to find a common denominator. Then I multiplyed the common denominator by both numerators where that part of the expression was already there. After I just had to solve and find the non-permmisble values.

Week 15 – Multiplying Rational Expressions

This week I learned how to multiply rational expressions.

Here is a common question:

This question asked me to simplify the expression. The first thing i did in this question was reduce the coefficients, and then I combined the two expressions together since it was multiplying. After I factored out what I could from the expression to figure out which factors can cancel out. Then i just reduced a to figure out my answer. The last step was to find out the non-permissible for a, and this means the values that will not make the denominator equal to zero. This is because in a division question you aren’t allowed to have the denominator  equal to zero.

Week 14 – Graphing Reciprocals of Quadratic Functions

This week I learned how to graph quadratic reciprocal functions.

Here is a common question:

This question asked me to figure out the parent function of the graph. I knew it was c, because I drew the parent graph by going through the invariant points. I also knew that the graph only had one root, because there was only two hyperbolas. Then I used 1,3,5 to draw the rest of the graph.

Week 13 – Graphing Reciprocal Linear Functions

This week I learned how to graph linear reciprocal functions.

Here is a common question:

This question asked me for each pair of functions, use the graph of the linear function to sketch a graph of the reciprocal function, and state the domain and range. First I sketched y = x + 2 by using the slope and the y intercept. Then i had to sketch the reciprocal of that function. First I figured out where the invariant points so I could draw the vertical and horizontal asymptotes. The graph never cross the asymptotes. Then I could sketch in the reciprocal of the graph. The domain and range are both elements of the real numbers, but they do not go through the origin of the graph, because there is no reciprocal for 0.