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?

Question

2363 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-01-04T09:32:29

Please see below.

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]}

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?