Flashcards in Calculus - P.1 Graphs and Models Deck (9)

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## Point-Plotting

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A. Table or T-chart to generate solution points or use transformation of parent graph

B. Plot points

C. Connect points with smooth curve

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## Intercepts

### Where the graph crosses the x-axis or y-axis

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## X-intercepts

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X-int: (a,0)

Let y=0 and solve for x

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## Y-intercepts

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Y-int: (0,b)

Let x=0, solve for y

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## Y-axis symmetry

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Any point, (a,b), on the graph will have a matching point (-a,b) on the graph.

Test => f(-x)=f(x)

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## X-axis symmetry

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If a point (a,b) is on the graph, then the point (a,-b) is also on the graph

Test => f(x)=_+f(x)

For each value of x, there are 2 values of y

Change y to -y will not change the function y=-y or f(x)=-f(x)

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## Symmetric about the origin

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If the point (a,b) is on the graph, (-a,-b) will also be on the graph

Test =>

f(-x)=-f(x)

f(-x)=-y

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## Points of intersection between two graphs

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1. Set one = to the other and solve. Plug answer into first equation to get both x and y => (x,y)

2. Solve as a System of equation => By substitution

3. Graph is indicated

Note: In some cases you may also solve by elimination

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