Chapter 6: Q. 100 (page 412)

Explain how you would scale the x-axis and y-axis before graphing $y = 3 \cos (πx)$ .

Short Answer

Expert verified

The x-axis will be scaled with multiple of $\frac{1}{2}$ units from the origin.

The y-axis will be scaled with multiple of $3$ units from origin.

Step by step solution

Step 1. Concept used

If $ω > 0$ , then the amplitude and period of role="math" localid="1646470212536" $y = A \cos ω x$ are given by

Amplitude $= |A|$

Period $= \frac{2 π}{ω}$

Step 2. Find the amplitude and period

Comparing the equation $y = 3 \cos (πx)$ to $y = A \cos (ω x)$ we find

$A = 3 ω = π$

So the amplitude is given as

$\begin{array}{rcl} |A| & = & |3| \\ = & 3 \end{array}$

and the period is given as

$\begin{array}{rcl} \frac{2 π}{ω} & = & \frac{2 π}{π} \\ = & 2 \end{array}$

Step 3. Find the scale

As the amplitude of the function is $3$ so the $y$ axis will be scaled with the multiple of $3$ units from the origin.

The period of the function is $2$ so the $x$ axis will be scaled with the multiple of $\frac{1}{2}$ units from the origin.

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Explain how you would scale the x-axis and y-axis before graphing $y = 3 \cos (πx)$ .

Short Answer

Step by step solution

Step 1. Concept used

Step 2. Find the amplitude and period

Step 3. Find the scale

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Explain how you would scale the x-axis and y-axis before graphing y=3cosπx.

Short Answer

Step by step solution

Step 1. Concept used

Step 2. Find the amplitude and period

Step 3. Find the scale

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Pure Maths

Decision Maths

Mechanics Maths

Probability and Statistics

Calculus

Geometry

Study anywhere. Anytime. Across all devices.

Explain how you would scale the x-axis and y-axis before graphing $y = 3 \cos (πx)$ .