I have a couple of questions about Chapter 2." "In a problem such as
1)
If (5, b) is a point on the graph of 4x - 5y = 12, what is b?
Would you solve it by letting x = 0
4(0) - 5y = 12
-5y = 12 divide by -5
y = -12/5
(5, -12/5) would that be the correct way to do that?
That wouldn't work.
Use the information you have.
(5, b) is a point on the graph. That means when x = 5, y = b.
So substitute 5 for x and b for y. You get
4 * 5 - 5 * b = 12.
Solve this equation for b. You get b = 8/5.
2)
Graph the function
y = 3x^2
Would you set up a table like
x y = 3x^2 (x,y)
-2 y = 3(-2)^2 (-2, -12)
repeating the process for other points for x such as -1, 0, 1, 2....
and then putting that on a graph and drawing a smooth curve through the points?
That would work. However note that (-2)^2 = (-2) * (-2) = 4, not -4, so that the point on your table would be (-2, 12).
However you need to be able to graph such functions using the techniques of the course, and extensive tables are not the way to do this.
The method as presented in the course is to graph the basic function, then use transformations (e.g., stretches and shifts) to obtain the graph of the given function.
In this case the basic function is y = x^2. It should be easy to verify that the graph of y = x^2 is a parabola, which can be defined by the three points (-1, 1), (0, 0) and (1, 1).
The graph of y = 3 x^2 is a vertically stretched version of the y = x^2 graph. Every point of the y = x^2 graph is moved three times as far from the x axis.
This transformation changes the points (-1, 1), (0, 0) and (1, 1) to the points (-1, 3), (0, 0) and (1, 3).