Question

Given that the point (−6,16) is on the graph of y=f(x), what is another point on the graph of y=−14f(x−3)−4 ?

I don't know how to find the other point on y=-14f(x-3)-4

Answer 1

`color(blue)((-3,-228)`

Explanation:

First we note that. For a function:

`f(x)` we obtain a horizontal shift if we add a constant `a` to the variable, in this case `x`.

Example:

`f(x)=x^2->f(x-a)=(x-a)^2`. If `a>0` then the function is shifted `bba` units in the positive x direction. If `a<0` then the function is shifted `bba` units in the negative `x` direction.

We now know that if we use the value `x=-6` in `f(x)` the output is `16`, but in `f(x-3)` the function has been shifted 3 units to the right, this means that we need to find a value `x`, so that

`x-3=-6`

`x=-3`

This can be seen as:

`f(x)->f(-6)=16`

`f(x-3)->(f((-3)-3)=f(-6)=16`

`y=-14(f(x-3)-4=>y=-14(16)-4`

`:.`

`y=-14(16)-4=-228`

So the point is:

`color(blue)((-3,-228)`