Question

Giselle graphs the function f(x) = x^2. Robin graphs the function g(x) = –x^2. How does Robin’s graph relate to Giselle’s?


Robin’s graph is a reflection of Giselle’s graph over the x-axis.

Robin’s graph is a reflection of Giselle’s graph over the y-axis.

Robin’s graph is a translation of Giselle’s graph 1 unit down.

Robin’s graph is a translation of Giselle’s graph 1 unit left.

Answer 1

I graphed the functions using 1,2,3 as the value of x.

My answer would be: Robin’s graph is a reflection of Giselle’s graph over the x-axis.

Answer 2

Robin's graph of the function $g(x)=-x^2=-f(x)$ is the reflection of Giselle’s graph over the x-axis.

You can think in two ways:

1. For the function y=f(x), the sign minus before f(x) change the positive values of y into negative values. For example, f(2)=4 and g(2)=-4. This means that graphs of f(x) and g(x) are symmetric across the x-axis.

2. You can simply construct the table of values

$\begin{array}{rcc} x & f(x)=x^2 & g(x)=-x^2 \\ 0 & 0 & 0 \\ 1 & 1 & -1 \\ -1 & 1 & -1 \\ 2 & 4 & -4 \\ -2 & 4 & -4 \\ 3 & 9 & -9 \\ -3 & 9 & -9 \end{array}$

and plot both graphs on the coordinate plane. From this diagram it is seen that graphs are symmetric over x-axis and Robin’s graph is a reflection of Giselle’s graph over the x-axis.