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).
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)...
-3
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
To translate the graph y = x to the graph of y = x - 6, shift the graph of y = x down 6 units.
The graph of g(x) is the graph of f(x) shifted 6 units in the direction of positive x.
g(x) = x-6 is the function g(x) = x with a negative vertical shift of 6. That is to say, take the whole graph of g(x) = x and move it down 6 units.
They are: 6 and -3
6
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).
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)...
The graph is a circle with a radius of 6, centered at the origin.
3
it will be an infinite region bounded by the lines x=2 and x=6
First of all, if 'x' is 3, then 'x' doesn't equal -3x+3 . You must mean y = -3x + 3.If x=3, then (-3x + 3) = -6 .The graph is the point (3, -6) .
-3