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-7 -6 -5 The PERIOD of a function is how long it takes (how far it travels ←horizontally→) before the pattern repeats itself. The period of the function above is 2 -4 -3 -2 -1 1 Period = 2 2 3 4 5 6 7 -7 -6 the period of this function is : units -5 -4 -3 -2 -1 Period 1 2 3 4 5 6 7 -7 -6 -5 Period = units -4 -3 -2 -1 1 2 3 4 5 6 7 -7 -6 3 units -5 Period = 3 units -4 -3 -2 -1 1 2 3 4 5 6 7 2 -2 4 -4 6 -6 π -π 2π -2π 3π -3π The period of this cosine function is 2π It repeats every 2π units 2 -2 4 -4 π -π 2π -2π -7 This graph is in RADIANS This is the function f(x) = sin x -6 Notice how π (3.14) is listed right after 3 -5 -4 -3 -2 -1 1 2 2 Period is: 3 π 4 5 2π 6 7 -7 -6 Zeroes occur at ...-4, 0, 4... Zeroes of this function occur where the graph hits the x-axis (where y=0) -5 -4 -3 -2 -1 1 2 3 4 5 6 7 -7 -6 Where is the zero in the interval [1,5] ? Zeroes of this function occur where the graph hits the x-axis (where y=0) -5 -4 -3 -2 -1 1 [ 2 Interval 3 4 x= ] 5 6 7 -7 [ Where is the zero in the interval [-7,-3] ? -6 Interval Zeroes of this function occur where the graph hits the x-axis (where y=0) -5 -4 -3 ] -2 -1 1 2 3 4 x= 5 6 7 -7 Where is the zero in the interval [-1,3] ? -6 Zeroes of this function occur where the graph hits the x-axis (where y=0) -5 -4 -3 -2 -1 [ Interval 1 2 ] 3 4 x= 5 6 7 -7 -6 The maximum value of this function is y= The maximum value of the function is where y is at its ↑ highest ↑ point -5 -4 -3 -2 -1 1 2 4 3 1 2 3 4 5 6 7 -7 -6 Maximum y = -5 -4 -3 -2 -1 1 2 3 4 5 6 7 -7 -6 The maximum value in the interval [-4,-2] is -5 -4 [ Interval -3 -2 ] y= -1 1 2 4 3 1 2 3 4 5 6 7 2 -2 4 -4 π -π 2π -2π -7 -6 -5 Period of this function: -4 -3 -2 -1 1 π 4 2π 2 3 4 5 6 7 2 -2 4 -4 π -π 2π -2π -7 -6 -5 Approximate zero of this function in the interval [0,4] -4 -3 -2 -1 1 1.57 1.95 2.23 2 3 4 5 6 7 2 -2 4 -4 π -π 2π -2π -7 -6 -5 Approximate maximum of this function in the interval [1,4] is y= -4 -3 -2 -1 1 -.5 .54 1 2 3 4 5 6 7 2 -2 4 -4 π -π 2π -2π -7 y=1 is the overall maximum, but it occurs when x=0, outside the[1,4] interval -6 -5 Approximate maximum of this function in the interval [1,4] -4 -3 -2 -1 [ 1 y= This interval only 2 3 .54 ] 4 5 6 7 The end (this is the graph of the secant function) |