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-

Elementary Algebra

17th Edition

ISBN:9780998625713

Author:Lynn Marecek, MaryAnne Anthony-Smith

Publisher:Lynn Marecek, MaryAnne Anthony-Smith

Chapter8: Rational Expressions And Equations

Section8.9: Use Direct And Inverse Variation

Problem 497E: If p vanes inversely with q and p=5when q=6 , find the equation that relates p and q.

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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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