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Graphs and Variables

DEPENDENT AND INDEPENDENT VARIABLES

A simple hypothesis may be: The more time a basketball player spends practicing penalty shots, the higher the percentage of penalty shots the player makes in competition. To verify the hypothesis, we directly manipulate practice time to see how it affects scoring penalty shots. The variable we directly manipulate is the independent variable, the other is the dependent variable.

Graphing Relationship Problems

Graphic relationships can be expressed as equations.

1. Name the relationship described by each of the lines or curves on this graph.

2. Write the general form of each relationship depicted in 1.

f = m v squared divided by r.

3. Given the relationship involving F, m, v, and R,
a. write the relationship between F and R; sketch a graph that shows the shape of the curve of a graph of F vs R.
b. write the relationship between F and v; sketch a graph that shows the shape of the curve of a graph of F vs v.
c. write the relationship between m and R; sketch a graph that shows the shape of the curve of a graph of m vs R.
d. In each of (a) to (c ), which variable is the dependent variable?
e. In each of (a) to (c ), which variable is the manipulated?
f. If F is centripetal force on an object traveling in a circle at constant speed, and R is the radius of the circle, write a simple hypothesis about centripetal force and radius consistent with (a) above.

Answers to Graphing Relationship Problems

1.
a. direct proportion
b. linear
c. linear
d. direct proportion
e. inverse
f. power
g. power

2.
a. y = mx
b. y = mx + b
c. y = mx + b
d. y = mx
e. y = 1/(xn)
f. y = mxn
g. x = myn

3.a.Graph of inverse relationship.

3.b.Graph of a portion of a simple parabola.

3.c.Graph of a simple linear relationship.

d. F, F, R
e. R, v, m
f. For a car turning an unbanked corner, the larger the radius of the curve, the smaller the turning force required.

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