If the following graph is of a function f(x)f(x), how will the graph of (i) f(x+3)f(x+3), (ii) f(x)+3f(x)+3, (iii) -f(x)−f(x) and (iv) 1-f(x-3)1−f(x−3) appear?

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1 Answer
Shwetank Mauria
Jan 4, 2017

Please see below.

Explanation:

The graph appears to be of a parabola y=f(x)=-x^2+2y=f(x)=−x2+2
graph{-x^2+2 [-5, 5, -2.5, 2.5]}

(i) y=f(x+3)=-(x+3)^2+2=-x^2-6x-9+2=-x^2-6x-7y=f(x+3)=−(x+3)2+2=−x2−6x−9+2=−x2−6x−7
graph{-x^2-6x-7 [-5.896, 4.104, -1.9, 3.1]}

(ii) y=f(x)+3=-x^2+2+3=-x^2+5y=f(x)+3=−x2+2+3=−x2+5
graph{-x^2+5 [-10.775, 9.225, -3.76, 6.24]}

(iii) y=-f(x)=-(-x^2+2)=x^2-2y=−f(x)=−(−x2+2)=x2−2
graph{x^2-2 [-10.73, 9.27, -2.2, 7.8]}

(iv) y=1-f(x-3)=1-(-(x-3)^2+2)y=1−f(x−3)=1−(−(x−3)2+2)
= 1+x^2-6x+9-2=x^2-6x+81+x2−6x+9−2=x2−6x+8
graph{x^2-6x+8 [-7.77, 12.23, -1.72, 8.28]}

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