Other Non-Linear Graphs

• Construct a table of values and draw the graph for cubic equation and simple sums of linear and non-linear terms;

• Construct a table of values and draw the graph of an exponential equations

• Interpret graph of higher order equations and use them to solve related equations

• Open geogebra.org/calculator

• Draw these functions: y=x³, y=-x³, y=2x³, and y=1/2x²

• State the characteristics of the graphs!

• Draw y=x³, y=x³-3 and y=(x-2)³-3

• State the characteristics of the graphs!

​Cubic graphs characteristics

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In general, cubic graph is y = ax³, where a determines the direction and how wide the graph is.

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The cube y = a(x-b)³​+c has:

• a value determines direction and how wide the graph is

• b value determines how many units the graph shifts to the right

• c value determi​nes how many units the graph shifts up and y-intercept

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• Using geogebra, draw y=2^x and y=2^-x

• Determine the x-intercept and y-intercept

• Draw y=2^x+3 and state the characteristics (asymptote, y-intercept)

​Exponential graphs characteristics

Subject | Subject

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In general, exponential graph is y = a^x, where a determines the direction and how wide the graph is.

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The exponential y = a^x​+b has:

• a value determines direction and how wide the graph is

• y-intercept = b + 1

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• We can determine the type of graph/curve by looking at the highest power

• The solution of the simultaneous equations is the intersection of the graphs (x-values)

• The red graph is y=2^x and the green one is y=3-x

• The intersection of the curve and the line is the solution for 3-x=2^x

• The solution/root is x=1

• The red graph is y=x and the purple one is y=x³

• The intersection of the curve and the line is the solution for x=x³

• The solution/root is x=-1, x=0, and x=1

• There are 3 intersection points, so there are 3 solutions/roots