Big Ideas Math Algebra 2, 2014
BI
Big Ideas Math Algebra 2, 2014 View details
3. Graphing Radical Functions
Continue to next subchapter

Exercise 59 Page 257

To graph the equation, first isolate y. You will have to graph two separate equations.

Graph:

Radius: 1
x-intercepts: ±1
y-intercepts: ±1

Practice makes perfect
Before we can use a graphing calculator to graph the given equation, we have to isolate y.
1-y^2 = x^2
- y^2=x^2 - 1
y^2 = - x^2 + 1
y^2 = 1 - x^2
y=± sqrt(1-x^2)
Next, to see this equation on a calculator, we actually have to use two separate functions. This is because a circle is not a function — think back to the Vertical Line Test.

y=sqrt(1-x^2) and y=- sqrt(1-x^2) To enter these functions, push Y= and type them in two different rows. Then push GRAPH to draw them.

Looking at the graph, we can see that the circle has a radius of 1. Also, both of its x- and y-intercepts occur at 1 and -1.