Graphs and Equation Relationships

[conquerDat]

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Can someone tell me how certain graphs are related to variable relationships?

For example linear graphs are straight lines.

How about an x= y^2 type graph, x = y^-1, x = y^fraction (squareroot)

I feel like if we know the relationships and how they look like on a graph, the graph problems will be easier to solve.

 

[Captain Sisko]

Can someone tell me how certain graphs are related to variable relationships?

For example linear graphs are straight lines.

How about an x= y^2 type graph, x = y^-1, x = y^fraction (squareroot)

I feel like if we know the relationships and how they look like on a graph, the graph problems will be easier to solve.

If you have access to excel you should just make some graphs and play around with it to see for yourself. pm me if you need help doing this, but it's worth going through the exercise- you won't forget it.

 

[sakabato93]

Can someone tell me how certain graphs are related to variable relationships?

For example linear graphs are straight lines.

How about an x= y^2 type graph, x = y^-1, x = y^fraction (squareroot)

I feel like if we know the relationships and how they look like on a graph, the graph problems will be easier to solve.

If you are using the standard axes for alebraic graphing (x as independent variable and y as dependent variable), then use these rules:

1.) Always solve for y first.
2.) Look at the degree of the x containing terms (degree is exponent of a monomial or the largest exponent of a polynomial function); if there is a algebraic operator/function like log or exponential, that supercedes the degree in determining shape
3.) Degree or operator/function will determine shape of the graph.

Ex) x=y^2

1.) Solve for y: y=x^(1/2) or y=x^(0.5)
2.) Degree: Degree of monomial is 1/2
3.) Graphs of degree 1/2 polynomial is shaped like half of a sideways parabola opening to the right

Remember this only works for functions of SINGLE variables.

I'd suggest typing common functions (quadratics, cubics, logs, exponentials) into a graphing calculator and studying the shapes of the graphs. Make sure that you only put in simple functions of those