This week in precalc 11 we learned about graphing reciprocal linear  and quadratic functions. When graphing reciprocal linear functions or quadratic functions, we need to understand and try to visualize what most functions will look like. Then we just follow the steps.

Reciprocal Linear:

-graph parent function ( using the slope and y-intercept)

-the x-intercept of the linear graph will become the vertical asymptote of the reciprocal

-find and mark the invariant points (every place where the original graph has a y-value of -1 or 1)

-graph the shape of a hyperbola based on the reciprocals of the y-values of the original function

Reciprocal Quadratic: 

-graph the quadratic function

-x intercepts become the vertical asymptotes

-locate and mark the invariant points. y= 1 or -1

-use a few other points to sketch the graph of the reciprocal

This week in precalc 11 we learned about absolute value functions.
An absolute value function is a function that has an algebraic expression within absolute value symbols in it.
*(the absolute value of a number is its distance from zero on a number line)*
The absolute value parent function is written as f (x) = | x | which is also defined as

f (x) = {x if x >0
0 if x = 0
-x if x < 0

We also learned how to solve equations with absolute values in it. There are some simple steps do to so. First, you isolate the absolute value expression, then you put the quantity inside the absolute notation equal to + and – the quantity on the other side of the equation
You then solve for the variable in both equations, and always remember to always check the answers to make sure you got the right answer and not an extraneous solution.
Here’s an example:
|2x-1| = 5
We write the equations with the different signs + and – and solve them.
|2x-1| = 5 and |2x-1| = – 5

1.) |2x-1| = 5
2x – 1 = 5
2x = 6
x = 3

2.) |2x-1| = – 5
2x – 1 = – 5
2x = – 4
x = – 2

The answers are 3 and – 2. To make sure we got the right answer, we check by substituting these answers into the original equation.

This week in precalc 11 we learned about graphing quadratic inequalities which is in the form of y > a + bx + c.

(the sign could be <,>,  ≤ , ≥)

We also learned how to graph linear inequalities in two variables.

First we need to rearrange the equation into the y = mx + b form. Then we use the y intercept and the slope to graph the points, we then connect these points into a straight line. depending whether the symbol is <> we use a broken line and if its ≥ or ≤ we use a solid line.
Finally we just color the side with the solutions, to do this we just pick a test point and use it on the original equation (usually 0,0 is a good test point), if the statement is true we shade in the side of the graph with the points if not we shade the other side.

This week in precalc 11 we had our chapter 4 unit test and our midterm. Some things I wish I studied a little more for the midterm was unit 2 and 3 where I know I was a little confused.

Then on Friday we had our first lesson on unit 5, where we were introduced to solving and graphing quadratic inequalities with one variable. With inequalities, we just solve the problem like a quadratic equation. First we factor, then we need to find the zeros of the equation, and then finally we need to test the numbers to make sure the statement is right.

Also one thing we were told to remember was that when we divide a negative inequality, you have to switch the sign.

This week in precalc 11 we learned about equivalent forms of a quadratic function. This just means finding different ways or representing a quadratic function to find more information about it. So we basically have

1.) Standard (Vertex) Form: y = a + q 

We can find the vertex

2.) General Form: y = a + bx + c

You can find the Y-intercepts

3.) Factored Form: y = a ( x – x1 ) (x – y2 )

You can find the X-intercepts

We also learned how parent functions transform . Here we have the vertex form y = a + q

The a in the equation will tell us if the parabola opens down or up, and if there’s a stretch or a compression. the p will tell us if there’s a horizontal translation and the q will tell us if there’s a vertical translation.