If the following graph is of a function #f(x)#, how will the graph of (i) #f(x+3)#, (ii) #f(x)+3#, (iii) #-f(x)# and (iv) #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+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-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+5#
graph{-x^2+5 [-10.775, 9.225, -3.76, 6.24]}

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

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

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