Knowing the type of graph by looking at the equation, makes it very easy to sketch a graph.

The following is a list of examples of a variety of graphs.

        Equation       Degree          Name             Shape         Description

1.      y = 7-3x                 x^{1}                   linear             straight line     / if x is +, \ if x is -

2.      y=x^{2}-2                 x^{2}                 quadratic         Parabola          opens up if x is +,  opens down if x is -

3.     y=x^{3}-4x               x^{3}                   cubic              wavy line          falls to the left and rises to the right if x is +, falls to the right and rises to the right if x is -

4.    y^{2}=x +4                 y^{2}                  quadratic          parabola        opens to the right if y is +. opens to the left if y is -

5.    y=\left | x-1 \right |                \left | x \right |                 absolute value     v shaped       upright v if +\left | x \right | . inverted v if -\left | x \right |

Describe the graph of the given equation.

a.  y=x^{2}-2x     — the graph is a parabola that opens up

b.  y=x^{3}-x+1   — the graph is a cubic wavy line that falls to the left and rises to the right

c.  y=1-x      — the graph is a straight line that slopes to the left

d.  y=\left | x \right |-3   –the graph is a v that opens up, the vertex is a point on the y-axis that is three units below the x-axis.

Filed under: Functions and Their Graphs

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