This week I started and finished the unit Inequalities (Systems & Graphs). In this unit, the questions began by having me manipulate inequalities, many of which took essentially the same form as linear equations (Slope Intercept form, Point Slope Form, and Standard Form), and had me solve for one or two variables. After having worked through so many similar types of questions in past units on linear equations, I didn’t find these questions to be all that difficult.

I then worked on graphing inequalities which I’ve also done in past units and didn’t find to be too tough. Key things to remember when graphing an inequality are:

• If the inequality uses a less-than (<) or greater-than (>) symbol, the line on the graph will be dotted
• If the inequality uses a less-than-or-equal-to or greater-than-or-equal-to symbol, the line on the graph will be solid
• If the inequality states that y is less-than or less-than-or-equal-to, the bottom half of the graph is shaded
• If the inequality states that that y is greater-than or greater-than-or-equal-to, the top half of the graph is shaded

Lastly in this unit, I worked through word problems which, as usual, I found to be the most difficult. It’s become evident that taking my time when working on word problems and writing everything down helps me substantially and makes it much more likely that I get the correct answer.

After finishing Inequalities (Systems & Graphs), I began the unit Functions. This was the first time in this course Algebra 1 that I started a unit which I had zero experience work with the material that it presented. At this point I’m still not confident in my understanding of functions but, as far as I have come to understand, a function (written as f(x) and pronounced “f of x”) takes an input, runs the input through the function, and produces an output. An example of this would be:

• Input – f(x)
• Function –
  • x^2 if x is even
  • x + 5 if x is odd
• Output –
  • f(2) = 2^2 = 4
  • f(3) = 3 + 5 = 8
  • f(4) = 4^2 = 16
  • f(5) = 5 + 5 = 10

As far as I can tell, inputs can be anything:

• f(a) = the next largest number that starts with the same letter as variable (a)
  • f(5) (F-ive) = 14 (F-ourteen)
  • f(8) (E-ight) = 11 (E-leven)

I find the language of these questions difficult to interpret. I need more practice reading these questions and working through them to get a better grasp on the terminology and phrasing used. An example of a question I found difficult was:

• For a given value r, the function h outputs a value q to satisfy the following equation:
  • q – 10 = 6(r + 1)
• Write a formula for h(r) in terms of r.
  • q = 6(r + 1) + 10
  • q = 6r + 6 + 10
  • q = 6r + 16, therefore
  • h(r) = 6r + 16

In the above example, I find the use of h(r) in place of q confusing. In my mind, the question is essentially saying “replace q with h(r)”. Learning more about the use of functions and their purpose, I’m sure, will help me comprehend the language/terminology used in these questions.

My goal in Week 12 is to get through the Functions unit. I’ve completed 560/2200 Mastery Points of it so far. There are 29 videos and 15 practice modules left for me to get through, and then the unit test on top of that. Time to get to work!