Gens Posted September 30, 2011 Share Posted September 30, 2011 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. Link to comment Share on other sites More sharing options...
Daedalus Posted October 1, 2011 Share Posted October 1, 2011 (edited) 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 Link to comment Share on other sites More sharing options...
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