a To draw a graph on your calculator, you first have to press Y= and write the function on one of the rows. Having written the function, you can press GRAPH to draw it.
B
b Interpreting the graphs in Part A, derive a rule for the symmetry of the graphs in the form of y=x^n.
A
a See solution
B
b See solution
Practice makes perfect
a To draw a graph on your calculator, we first have to press Y= and write the function on one of the rows. Having written the function, we can press GRAPH to draw it. In order to more clearly see the difference between the graphs, we will look at only three at a time.
Next, we will graph the next group of functions proceeding in the same way.
Looking at the graphs, we can see that y=x, y=x^3, and y=x^5 are all symmetric with respect to the origin. y=x^2, y=x^4, and y=x^6 are all symmetric to the y-axis.
b Interpreting the graphs in Part A, we can generalize the symmetry of the graphs in the form of y=x^n.
If n is odd, then the symmetry of y=x^n is the origin.
If n is even, then the symmetry axis of y=x^n is the y-axis.
Therefore, y=x^(10) is symmetric with respect to the y-axis and y=x^(11) is symmetric to the origin. Let's graph them to verify our predictions.
