Inverse Functions Example 1
Its graph would be a straight lineFor example, y > x 2;
Y as a function of x graph examples
Y as a function of x graph examples-Plot(x, y), axis(0 10 1 1)Plot the graph for "y=x2" line by putting the values for x Remember to draw a solid line for y≤ or y≥ and a dashed line for y< or y> Now, shade the line as per inequalities, such as above the line for a "greater than" (y> or y≥) and below the line for a
Graphing Square Root Functions
For example, for the cubic function y = x^3, the original graph looks like this The translation equation, y = (1(x^3 1)) 1, which has 1 for b, 1 for c, and 1 for d but has no value for a, looks like this Incorrectly putting a 0 in for the a value for a produces this equation y = 0(1(x^3 1)) 1 and looks like thisThe xintercept is the point where the graph of the plotted line crosses the xaxis On the graph below, the plotted line crosses the xaxis at x = 5 Eyeballing the graph isn't an exact method For example, in the graph above, the actual xintercept could fall somewhere between 49 and 51A coordinate grid has two perpendicular lines, or axes, labeled like number lines The horizontal axis is called the xaxis The vertical axis is called the yaxis The point where the xaxis and yaxis intersect is called the origin
A graph is a visual representation of a relationship between two variables, x and y A graph consists of two axes called the x (horizontal) and y (vertical) axes These axes correspond to the variables we are relating In economics we will usually give the Graph Quadrants Quadrant Numbers on a Graph The previous section introduced the terms xaxis and yaxisThe values of these two axes are key to understanding the quadrants and how they are labeled For example, the graph of a circle centered at the origin exhibits all three symmetries Tests for Symmetry We've some fairly simply tests for each of the different types of symmetry A graph will have symmetry about the \(x\)axis if we get an equivalent equation when all the \(y\)'s are replaced with –\(y\)
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Example 1 Graph the equation of the line 2 x − 4 y = 8 2x4y=8 2x − 4y = 8 using its intercepts I hope you recognize that this is an equation of a line in Standard Form where both the x and y variables are found on one side of the equation opposite the constant termIts equation will be an exponential function y = 6 x y = 6 x y=6^x y = 6 x is an exponential function y = 6 x 1 y = 6 x 1 y=6x1 y = 6 x 1 is a linear function;
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