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Semmy [17]
3 years ago
11

Determine if the graph is symmetric about the x-axis, the y-axis, or the origin.

Mathematics
2 answers:
Alexandra [31]3 years ago
7 0
Answer: y-axis.

Explanation:

The equation <span>r = 3 - 4 sin θ may be graphed using cartesian coordinates (i.e. x and y) or polar coordinates.

The logical way is to graph in polar coordinates. I did it using </span>a graphing software and obtained the attached graph.

Also, I attached the graph in cartesian coordinates.

Here you have a table that you can build by your self and use the pairs to draw the graph (either cartesian or polar coordinates).

<span> <span><span> θ (rad)    r = 3 - 4 sin θ </span> <span>

0               3 </span> <span>
π/8            2.61731657 </span>
<span> π/4            2.29289322 </span> <span>
3π/8          2.07612047
</span> <span> π/2            2
</span> <span> 5π/8          2.07612047 </span> <span>
3π/4          2.29289322 </span> <span>
7π/8          2.61731657 </span> <span>
π               3 </span> <span>
9π/8          3.38268343 </span> <span>
5π/4          3.70710678 </span> <span>
11π/8        3.92387953 </span> <span>
3π/2          4 </span> <span>
13π/8        3.92387953 </span> <span>
7π/4          3.70710678 </span> <span>
15π/8        3.38268343 </span> <span>
2π             3 </span> </span></span>

In both of the attached graphs you can see that the left side is equal to the right side, but the upper side is not equal to the bottom side.

Therefore, the graph is symmetric about the y-axis.





Ghella [55]3 years ago
6 0

Answer:

y-axis... just look at the graph on desmos.com

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Answer:

Like terms, functions may be combined by addition, subtraction, multiplication or division.

Example 1. Given f ( x ) = 2x + 1 and g ( x ) = x2

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Solution

Step 1. Find ( f + g ) ( x )

Since ( f + g ) ( x ) = f ( x ) + g ( x ) then;

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2

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Step 2. Find ( f + g ) ( 2 )

To find the solution for ( f + g ) ( 2 ), evaluate the solution above for 2.

Since ( f + g ) ( x ) = x2

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Example 2. Given f ( x ) = 2x – 5 and g ( x ) = 1 – x find ( f – g ) ( x ) and ( f – g ) ( 2 ).

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Step 1. Find ( f – g ) ( x ).

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Example 3. Given f ( x ) = x2

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Step 1. Solve for ( f g ) ( x ).

Since ( f g ) ( x ) = f ( x ) * g ( x ) , then

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Example 4. Given f ( x ) = x + 1 and g ( x ) = x – 1 , find ( x ) and ( 3 ). f

g

⎛ ⎞ ⎜

⎝ ⎠

f

g

⎛ ⎞ ⎜

⎝ ⎠ ⎟ ⎟

Solution

Step 1. Solve for ( x ). f

g

⎛

⎜

⎝ ⎠

⎞

⎟

Since ( x ) = , then ( )

( )

f x

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f

g

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⎜

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⎞

⎟

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1

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x

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−

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=

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+

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g

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=

4

2

= 2

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