Write the function rule for each graph с.-2T-3m2-TT/23m22TT-1--2 d.-2m-3n/2-T/2-TT/23π/227-2-5

Answered: с. 2 -3m2 -T/2 TT/2 3m2 -1-

Algebra: Structure And Method, Book 1

(REV)00th Edition

ISBN:9780395977224

Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole

Publisher:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole

Chapter4: Polynomials

Section4.4: Powers Of Monimials

Problem 42WE

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Question

Write the function rule for each graph

Expert Solution

Step 1

Amplitude is the vertical distance between the midline and one of the maximum or minimum points. We can measure the height from highest to lowest point divide by 2.

Period is the distance between two consecutive maximum points, or two consecutive minimum points.

Midline is the horizontal line that divides the graph's maximum and minimum points into two halves.

Step 2

c) Consider the graph:

$\begin{matrix} Amplitude, |a| = \frac{maximum - minimum}{2} \\ a = \frac{1 - (- 1)}{2} \\ a = |\frac{- 2}{2}| \\ a = 1 \\ Period,b = \frac{2 π}{Distance between two maximums/or minimums} \\ = \frac{2 π}{|\frac{- 3 π}{4}| + |\frac{π}{4}|} \\ = \frac{2 π}{π} \\ = 2 \\ Midline (c), y = 0 \end{matrix}$

The graph is in the form:

$The function is in the form of f (x) = a \sin (b x) + c$

Substitute the values and find the equation:

$f (x) = \sin (2 x)$

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