This week, we learned about function notation. In this blog post, I am going to demonstrate how to understand and solve function notation.

Let’s say we had an equation that looked like this:

F(x) = 3x+4    F(3)

The F(x) notation is another way of showing the y value of a function. Because F(x) = y.

This is showing that we need to find the answer for the equation if X is equal to three.

The equation would end up looking like this:

(3)(3)+4

Which is equal to 13

Now 13 is representing our Y value. Because writing F(x) = 13 is the same thing as writing y = 13

Once you understand the steps of function notation, it is easy to solve these questions.

This week, we started to learn about relations. I thought that Domain and Range was really interesting and easy to understand once you have learned about it. In this blog post, I am going to talk about Domain and Range.

Domain: The domain of a function is the complete set of possible values of the independent variable.

Range: he range of a function is the complete set of all possible resulting values of the dependent variable.

Domain is always the X value and range is always the Y value. ( X is red and Y is blue).

If the relation is discrete, the domain and range would look something like this:

{X|0,3,-3,2} {Y|2,4,-2,}

If the relation is continuous but had a determined end the domain and range would look something like this:

{X|-3<X<3, XER} {Y|-2<Y<4, YER}

If the relation is continuous but didn’t have a determined end the domain and range would look something like this:

{X| XER} {Y| YER}

This week, we finished our polynomial unit test and learned how to solve “ugly trinomials”. These are expressions that are not are not able to be easily solved by just looking at them or using any of the four hints to factoring polynomials. In this blog post, I am going tok show you some tips and tricks to help you efficiently find the answer to these difficult expressions.

Step 1: Lets say you have an expression that looks like this

First thing first, we can see that there is a 3 to the power of 2 at the start of the expression. Draw out your two bracketed areas, place a 3x at the start of the first bracketed area and an x at the start of the second bracketed area. Example: (3x    )(x     )

Step 2: Looking at the last number of the expression, we are going to find any multiples of that particular number. In this case, the only multiples of 8 would be 1,8 and 2,4.

Step 3: This step is basically trial and error. You take each pair of numbers and try them in different orders in the blank areas within the brackets. You also need to figure out whether the numbers you are using should be negative of positive. You will know if you have chosen the right pair and placed them correctly by using the claw method to then expand the equation. if the two new numbers you get from expanding the equation equal to the middle monomial in the equation (in this case it is -2x), then you know that you have correctly solved the question.

The answer to this equation is (3x+4)(x-2)

This week we learned different methods you can use to to multiply to monomials to create a trinomial. In this blog post I am going to show you how to use the the distributive method because I find it the easiest and most efficient way to find your answer.

Let’s say you have an equation that looks like this:

(7x+9)(5x+2)

This is where you can use this method. All you have to do is multiply the different terms in a specific pattern.

This photo shows which terms need to be multiplied together, in what order (Blue 1st, red 2nd, green 3rd and black 4th).

If done correctly, your answer should look like this:

+ 14x + 45x + 18

Then you add your like terms together:

+ 59x + 18