Algebra: Chapter 12 Review
A RELATION is a set of ordered pairs, a FUNCTION is a relation that assigns to each member of the DOMAIN (`x`) exactly one member of the RANGE (`y`).
- Remember the VERTICAL LINE TEST to determine a FUNCTION!
- A LINEAR FUNCTION is of the form `y = mx + b`
- A QUADRATIC FUNCTION can be written `y = ax^2 + bx + c`
- DIRECT VARIATION: `y = kx`
- INDIRECT VARIATION: ` y = k/x`
- JOINT VARIATION: `y = kxz` or `y = kx/z`
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Algebra 1a: Chapter 9, Lesson 6, page 421.
Graphing Systems of Linear Inequalities
We continue Chapter 9-5 techniques and solve 2 inequalities.
For the first equation, we can use any technique we learned from Chapter 7. Usually, the slope-intercept or `x` and `y` intercepts can be used to quickly define the line. Check a simple point like `(0, 0)` to see if that part of the ½ plane is true. If so, then shade that area.
Do the same for the other inequality and shade the appropriate ½ plane. The IMPORTANT PART is WHERE THE 2 INEQUALITIES OVERLAP THEIR SHADING, IS THE SOLUTION TO BOTH INEQUALITIES.
Remember, boundary lines of the form `<` or `>` are DASHED. The line is NOT part of the solution. Lines of the form `≤` or`≥` are solid because their line ARE part of the solution.
Again, the textbook is pretty good here but here are some more examples from purplemath.com too!
Two of tonight’s homework problems solved by MrE are here! Just click it.