Find the Amplitude, Midline, Midline, period and Asymptotes for f(x)=−cot⁡13(x)+2

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Find the Amplitude, Midline, Midline, period and Asymptotes for  f(x)=−cot⁡13(x)+2

Orlando Paz · Accepted Answer

Step 1  f(x)=−cot⁡(x2)+2  f(x)=Acot⁡(Bx)+D  Midline is y=2 line  the vertical shift of 2 units up.  A=−1  Amplitude =|−A|=|−1|=1  Amplitude =1  Step 2  B=12  period =2πB  =2π12  Period =4π  In analytic geometry, an asymptote of a curve is a line such that the distance between the curve and the line approaches zero as one or both of the x or y coordinates tends to infinity.  Now, finding values of x for which cot⁡(x2) goes to infinity;  x2=nπ where, n∈Z  Asymptotes:  x=2nπ where n∈Z

Navreaiw · Accepted Answer

Find the asymptotes. No Horizontal Asymptotes No Oblique Asymptotes Vertical Asymptotes: x=π+2πn where n is an integer Use the form acot⁡(bx−c)+d to find the variables used to find the amplitude, period, phase shift, and vertical shift. a=−2 b=x2 c=0 d=0 Since the graph of the function cot does not have a maximum or minimum value, there can be no value for the amplitude. Amplitude: None Find the period using the formula π|b| Period: 2π Find the phase shift using the formula cd Phase Shift: 0 Find the vertical shift d Vertical Shift 0 List the properties of the trigonometric function. Amplitude: None Period: 2π Phase Shift: 0 (0 to the right) Vertical Shift: 0 Select a few points to graph. xf(x)00π2−23π222π05π−2 The trig function can be graphed using the amplitude, period, phase shift, vertical shift, and the points.

Find the Amplitude, Midline, Midline, period and Asymptotes for f(x)=-\cot\frac{1}{3}(x)+2

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