Week 3

During week 3, we continued in the chapter Functions. Since this week was only a four day week due to Labor Day, we only covered three lessons instead of four.

On the first day, we started with the lesson Symmetry and Transformations. We first looked at the power functions of each different type of equation. 

All Power functions start with f(x)=x^n

Below are examples of the ones we looked at. 

We then looked at how to tell which function is an even or an odd function. Even functions are symmetric to the y-axis and to find the symmetry of the y-axis is by turning x into -x. To find the odd functions, you find if it is symmetric to the origin, which is by turning both x and y functions into negatives.

We then looked at vertical and horizontal shifts. Below are the examples of shifting.

y=f(x)+c

y=f(x)-c

y=f(x+c)

y=f(x-c)

We then looked at reflections. To reflect on the x-axis, all you do is by putting the - on the outside of f(x). So it looks like -f(x). To reflect on the y-axis, you put the negative inside like f(-x). Then after, there are vertical streches and compressions. 

y=cf(x)

c>1 stretched or skinny

0<c<1 compressed or fat

This is what we worked on, on day one.

On Day two, we began Linear Functions. The first thing we saw was the constant function, which is y=b. The Linear function is f(x)=ax+b or y=mx+b.

Slope is m= y2-y1/x2-x1 which results in rise over run.

The Point slope equation is: y-y1=m(x-x1)

We then looked at increasing and decreasing. Some graphs have lines that go up like a parabola, yet they also have some that go down, which a parabola does as well and sine or cosine equations.

The slope intercept equation is y=mx+b, which is what we looked at earlier and a horizontal graph is y=b, while a vertical graph is x=a, which is usually an undefined slope. Parallel lines also have the same slope while perpendicular lines turn the slope into the negative reciprical. For example 3 turns into -1/3. 

Lastly, To find the points of intersection, you use substitution or elimination, which goes back to Pre-algebra. You plug in either y or x for the other equation for substition to solve and you find (x,y). 

This is what was learned on day 2.

On day 3, we first had a quiz and then we looked at quadratic functions. Most of the material we have looked at this section is review and this was no exception. 

The quadratic equation is: f(x)= a(x-h)^2 +k

To find the vertex (h, k). Ignore the negative

Axis of symmetry is x=h

to figure out if the equation is up a>0

to figure out if the equation is down a<0

We looked at how to make problems easy to solve by looking at which ones are the vertex or AOS by turning problems back into the original problem look.

Two examples are below:

After we looked at some examples, she left us off with information from Physics, which is Free Falling Objects.

This is what we did this week.
See you next week!