Algebra Know-It-ALL
If a point lies exactly on one of the axes or at the origin, then it is not in any quadrant. The quadrants are sometimes labeled ...
226 The Cartesian Plane Are you confused? The coordinate planes in Figs. 14-1, 14-2, and 14-3 show values only to up to ±6 for e ...
Positive/negative square root The second of the three relations we evaluated in Chap. 13 took the positive or negative square ro ...
228 The Cartesian Plane –6 –2–4 2 6 2 4 6 –2 –4 –6 x y (4,2) (4,–2) (0,0) (1,1) (1,–1) Figure 14-5 Cartesian graph of the relati ...
determined. There are computer programs that generate detailed graphs of relations by plotting millions of points and connecting ...
230 The Cartesian Plane When we want to graph the inverse of a relation, we “flip the whole graph over” along a “hinge” cor- res ...
Three Relations 231 –6 –4 –2 246 2 4 6 –2 –4 –6 x y (0,0) (1,1) (2,4) Figure 14-10 Cartesian graph of the relation y= (+x)^2. –6 ...
232 The Cartesian Plane Three Functions The process for graphing a function is the same as it is for graphing a relation. Rememb ...
–6 –4 –2 246 2 6 –2 –4 –6 (0,0) (–1,1) (1,1) (–2,4) (2,4) v w Figure 14-12 Cartesian graph of the function w=v^2. –6 246 t u 20 ...
234 The Cartesian Plane Note the difference in “magnification” between the t and u axes. This difference makes the graph fit nic ...
Imagine an ordered pair (x,y), and suppose we have plotted its point on the Cartesian plane. Where, in relation to the point fo ...
236 CHAPTER 15 Graphs of Linear Relations We’ve seen the graphs of some relations and functions. Now it’s time to focus on the g ...
Sometimes the slope of a straight line is informally called rise over run. This notion works as long as the independent variable ...
238 Graphs of Linear Relations Switching the order We can switch the points (x 1 ,y 1 ) and (x 2 ,y 2 ) and still get the same s ...
where a and b are constants. If you substitute y for 0 and then transpose the left and right sides, you get an equation for a li ...
240 Graphs of Linear Relations Here’s a challenge! Put the following equation into SI form as a linear function of x, and graph ...
we must know the coordinates of another point. We can find one by moving horizontally to the right by any number of units we wan ...
242 Graphs of Linear Relations Solution Table 15-1 is an S/R derivation of a SI equation from the standard form of a two-variabl ...
dard PS equation, we get y − 2 = 2[x − (−1)] which simplifies to y − 2 = 2(x+ 1) We can now find another point on the graph by p ...
244 Graphs of Linear Relations Are you confused? The PS form of a linear function is actually a generalized version of the SI fo ...
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