Corresponding points on the graph

[Gens]

Point P(2,3) is on the graph of f, find the corresponding point on the graph of y=-3f(x+2)-4

 

I have it solved, but I don't understand how to solve it.

What I have:

P(2,3)---> (0,-13)

y values multiplied by -3 and subtract 4

x values minus 2

 

Can somebody explain the process in details please.

[Daedalus]

To answer you question:

 

The point, [math]P(2 ,3)[/math] is produced by [math]f(x)[/math] such that [math]f(2)=3[/math].

 

You have been asked to find the corresponding point on [math]y=-3 \, f(x+2)-4[/math]. This means that the graph / function has been shifted to the left two units along the X axis, scaled by [math]-3[/math] and shifted down by [math]4[/math] units along the Y axis.

 

You can see that [math]f(x+2)[/math] shifts [math]f(x)[/math] to the left two units. So you have to set [math]f(x+2)=f(2)[/math] and solve for [math]x[/math]. This is done by setting the inputs equal to each other, [math]x+2=2[/math]. This gives you the corresponding X value which now equals zero. Ex. [math]f(0+2)=3[/math].

 

Since you know that [math]f(2)=f(0+2)=3[/math], you can solve for the corresponding Y value by multiplying the output [math]3[/math] by [math]-3[/math] and subtracting [math]4[/math] from the result which equals [math]-13[/math]:

 

[math]f(2)=f(0+2)=3[/math]

[math]y=-3 \, f(x+2) - 4=-3 \, f(0+2) - 4=-3 (3)-4=-13[/math].

 

This gives you the answer that you have:

 

[math]P(2, 3) \rightarrow P(0, -13)[/math]

 

I hope that helps : )

Edited October 1, 2011 by Daedalus