Graphs

Determine the intercepts and graph each equation by hand by plotting points. Verify your results using a graphing utility. Label the intercepts on the graph. 

$x^2+2y=16$.

Test each equation for symmetry with respect to the x-axis, the y-axis, and the origin. 

$2x=3y^2$.

Test each equation for symmetry with respect to the x-axis, the y-axis, and the origin.  

$x^2+4y^2=16$.

Test each equation for symmetry with respect to the x-axis, the y-axis, and the origin.

$y=x^4-3x^2-4$.

Test each equation for symmetry with respect to the x-axis, the y-axis, and the origin. 

$y=x^3-x$

Test each equation for symmetry with respect to the x-axis, the y-axis, and the origin. 

$x^2+x+y^2+2y=0$.

Sketch a graph of  $y=x^3$

Use a graphing utility to approximate the solutions of each equation rounded to two decimal places. All solutions lie between $-10$ and $10$.

$x^3-5x+3=0$.

Use a graphing utility to approximate the solutions of each equation rounded to two decimal places. All solutions lie between $-10$ and $10$.

$x^4-3=2x+1$.

Find an equation of the line having the given characteristics. Express your answer using either the general form or the slope–intercept form of the equation of a line, whichever you prefer. Graph the line.

Slope $=-2$; containing the point $\left(3,-1\right)$.

Find an equation of the line having the given characteristics. Express your answer using either the general form or the slope–intercept form of the equation of a line, whichever you prefer. Graph the line.

Slope $=0$; containing the point $\left(-5,4\right)$.

Find an equation of the line having the given characteristics. Express your answer using either the general form or the slope–intercept form of the equation of a line, whichever you prefer. Graph the line.

Slope undefined; containing the point $\left(-3,4\right)$.

Find an equation of the line having the given characteristics. Express your answer using either the general form or the slope–intercept form of the equation of a line, whichever you prefer. Graph the line .

x- intercept $=2$; containing the point $\left(4,-5\right)$.