Graph of Equation, Intercepts, Symmetry
1. Which of the following points \(\displaystyle{\left(-3,-\frac{1}{3}\right); (1,1);
(0,0); \left(-\frac{1}{5},5\right)}\) are on the graph of \(\displaystyle{y =
\frac{1}{x}}\) ? solution
2. Graph each equation by plotting points
\(\displaystyle{x = -3, -2, -1, 0, 1, 2, 3}\).
solution
(a) \(\displaystyle{y = |x - 1|}\)
(b) \(\displaystyle{y = \sqrt{9-x^2}}\)
3. Find the \(\displaystyle{x}\)- and \(\displaystyle{y}\)- intercepts of the graph of
the equation algebraically.
solution
(a) \(\displaystyle{3x-2y=6}\)
(b) \(\displaystyle{y = x^2 - 7x + 12}\)
(c) \(\displaystyle{\frac{2x}{5} + \frac{y}{3} = 6}\)
4. Test the following equations for symmetry with respect to the
\(\displaystyle{x}\)-axis, the \(\displaystyle{y}\)-axis, and the
origin. solution
(a) \(\displaystyle{y=x^3-x }\)
(b) \(\displaystyle{4x^2-y^2=5}\)
5. Find the center and radius of the circle \(\displaystyle{
x^2+y^2 -6x +8y -7 = 0} \).
solution
6. Find the center and radius of the circle \(\displaystyle{
3x^2+3y^2 +12y +3 = 0} \).
solution
7. Find the standard form of a circle with center at \( (2, -3 )\)
and radius of 4.
solution