This week in PreCalc 11 we revisited the idea of rational expressions and learned how to add together rational expressions with variables in the denominator.

for example:

when we add the rational expressions together the denominator needs to be the same so we take a common factor of the two denominators.

And we always need to remember that the denominator connot equal 0. So if the denominator is 8x x cannot equal 0. And if it is 8 + x, x cannot equal -8.

example:

6/5x + 4/3x

we would find the common factor of both denominators which in this case is 15 so we would multiply the top and bottom so the bottom equals 15

6/5x + 4/3x -> 18/15x + 20/15x

and then we could add them together

18+20/15x

38/15x is your answer

and if you could from this step you could simplify this expressions. (notice there isn’t an equal sign because expressions don’t contain equal signs)

last we need to write the restrictions for x so in this case x cannot equal 0.

This week in pre calc 11 we learned how to determine the difference between and absolute value graph and reciprocal value graph.

we know that an absolute value graph cannot have any negatives at all because when a number is in the absolute value symbol even if it is negative it must change to positive, that’s one way we can tell it is an absolute value graph, another way is that it will make a V shape if it is linear

ex:

and if it’s a quadratic function graph it will make a W shape

ex:

that is unless it is a horizontal line.

To tell if it is a reciprical you will notice that it will go in the negatives in most cases

ex:

ex:

This week in PreCalc 11,

we learned how to graph absolute value functions.
An Absolute Value Functions is a function that has an expression within absolute value symbols. We were taught before that Absolute Values, was when the number is between the absolute value symbols must come out a positive. Example, | -2 | = 2 .

Example:
y = | -2x + 4 |
Step 1: Graph the Parent Function
The first step is to graph the parent function. The parent function is the same function but without the absolute value symbols.

In this case, the parent function is y = -2x + 4.

Step 2: change the Negative Values to positive
y-values in the parent function can’t be negative that’s why there’s an absolute value function. So all we have to do is change the negative y-values into a positive and then graph it again.

and as u can see the parent function is shown in this graph but where it intercepts with the x intercept is where it bounces back up.

This week in Pre Calc 11,

We learned how to solve systems of equations using substitution.

A way to solve a linear system or quadratic system or both is to use the substitution method.

We do this by substituting a y-value in an equation with the other. to start you first substitute y in the second equation with the first equation (since y = y). Because it is harder to solve an equation if it has two variables. After substituting y into the equation and solving for x, the value of x can then be used to find y by substituting the number you found, with x. While using the substitution method, you can also start by substituting x in the second equation with the first equation. You can start of by substituting x first or y your choice.
For example :
y = 2x + 2
y = x^2 + 5x +4
Take the first equation and replace it with the y in the second.
2x + 2 = x^2 + 5x +4
Solve for x.

0= x^2+3x+2

0= (x+3)(x+1)