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Given that (7-6) is on the graph f(x) find the corresponding point for the function f(x plus 2)?
When the x coordinate is changed by adding a constant amount this is the same as translating (shifting) the graph of the function f(x) that amount parallel to the x-axis; if the amount is positive the graph is translated to the left, if it is negative it is translated to the right. As (7, -6) is on f(x), then under the translation f(x + 2), the graph is translated to the left (2 x-values), so the point (7-2, -6) which is the point (5, -6) is the corresponding point on the graph to (7, -6).
How do you go about creating a graph with specific x intercepts like say at x equals -2 4 and 6?
If you want the graph to cross the x-axis at x = -2, then (x+2) is going to be a factor of the equation of the line. If you want the graph to cross the x-axis at x = 2 and x = 6, then the two factors will be (x-2) and (x-6) and the equation of the line will be y = (x-2)(x-6). This simplifies to y = x2-8x+12. In general, if you want to plot a graph with a line that crosses the x-axis at points x=a, x=b, x=c, x=d, ... where a,b,c,d... are integers, the equation of the line will be: y = (x-a)(x-b)(x-c)(x-d)...
How would you graph the solution to x 4 -2?
6
How do you graph 3y-x equals 6?
-3
Graph x plus y equals 6?
The easiest way to do this would be to put the equation for y in terms of x. We have x+y = 6 subtracting x from both sides gives y = 6 - x This is of the form y = ax + b where b is 6 and a is minus 1. So the graph will be a line, with gradient minus 1, that crosses the y axis at y=6
