Given the coordinate point (-3,5) on f(x), transform the coordinate point using the rules for h(x) and g(x). Compare the results and explain your findings.

Answer 1

This seems quite a tricky way of asking the question, but I believe it's about points on/off a line, and where the lines cross each other.

As I don't have your functions, I'll make some up, using another point.

If you recall, the form of straight line is y =mx + c where m is the gradient, and c is the y intercept.

My point is (0,0) the origin.

My f(x) will be y = x which I know [because same as y = 1x + 0] passes through (0,0) (1,1) (2,2) etc

My g(x) I need to also pass through same point so I will use y = -x [y = -1x + 0]. Which points will it pass through?

My h(x) is a third line which WILL NOT go through the origin. I have infinite options, but I'll pick y = x+2 which passes through point (0,2) and is parallel to f(x). (How do I know it's parallel?)

As an extra, I'll add function p(x) which is x = 0. What does this line look like?

So then take the point (0,0) and substitute ("transform the coordinate point using the rules") in the functions:

f(x) is y = x so 0 = 0 [true]

g(x) is y = -x so 0 = -0 [true because -0 is 0]

h(x) is y = x+2 so 0 = 2 [false]

p(x) is x = 0 so 0 = 0 [true]

Let's take point (0,2) and do the same:

f(x) is y = x so 2 = 0 [false]

g(x) is y = -x so 2 = -0 [false]

h(x) is y = x+2 so 2 = 2 [true]

p(x) is x = 0 so 0 = 0 [true]

Hence, hopefully, you can see that when you plug a point into a function, you can see whether that particular point lies on the line (true) or not (false). And if one point lies on two lines (both true), then those lines intersect. In my example above, you can see 3 lines cross (0,0) and 2 functions intersect at (0,2).