Within the following applet, change the slider values for " a", " h", and " k".Īs you do, pay attention to how the equation of the graph changes as you use the slider to change a certain parameter.īe sure to pay close attention as you change parameters, one at a time, for EACH of the four functions listed below.Īfter interacting with this applet for a few minutes, answer the questions (below the applet) as specifically as you can. Instead, use the average force: The force varies uniformly from 0 to kx, so the average force is kx/2. In the equation Work Force Distance, the force is changing so you cant just put F kx, since thats only true when the spring is fully stretched. The following applet allows you to use a slider to change the values of different parameters of 4 key functions. Even without calculus you should be able to see where the half comes in. In each of these functions, you will investigate what the parameters "a", "h", & "k" will do to the graph the parent function y = f(x) when we graph the function y = a*f(x - h) + k You can see that the function has three zeroes as. Adding k to the function translates the graph upwards ( k > 0) or downwards ( k < 0 ). With corresponding values f (1) 1 3 2 for the minimum and f ( 1) 1 +3 2 for the maximum. The basic square root function: y = sqrt(x) The minimum and maximum are found by posing. The basic absolute value function: f(x) = |x| As shown in the previous section, power functions are functions in the form of f(x) kxa or y kxa, where k is a nonzero coefficient, and a is a real. The following applet allows you to select one of 4 parent functions: Recognizing a pattern, such as the difference of squares. Expanding (the opposite of factoring) may also help. Divide every term by the same nonzero value. We can directly obtain the spring constant k k k k from the Young's modulus of the material, the area A A A A over which the force is applied (since stress depends on the area) and nominal length of the material L L L L. Clear out any fractions by Multiplying every term by the bottom parts. Young's modulus can be defined at any strain, but where Hooke's law is obeyed it is a constant. We're going to refer to this function as the PARENT FUNCTION. Add or Subtract the same value from both sides.
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