Question

Suppose that the graph of f contains the point 5,2. Find a point that must be on the graph of g(x)=3f(x+7)

Answer 1

`\bf \begin{cases} f(x)\qquad (\stackrel{x}{5},\stackrel{y}{2})\\\\ g(x)=3f(x+7) \end{cases}`

if we substitute "x" for "x+7", that's is just a horizontal shift of 7 units, to the left, so the x-coordinate in f(x) of 5, will move 7 units to the left then, or 5 - 7 = -2.

now, the point itself has moved horizontally 7 units, that means the y-coordinate of 2 moved as well, 2 - 7 = -5.

so the new location for 5,2 is at -2, -5.

then the "3" shrinkage,

3(-2) = -6 <---- x-coordinate,

and 3(-5) = -15 <---- y-coordinate

so, the new location for 5,2 with the translations in g(x), is at (-6, -15)