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
