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nth term a_{n}=3^{n-1}

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f(x)=(4x³−x²+x−2)−(−x²+3)

Solution

Domain: −∞ <x<∞

Range: −∞ <f(x)<∞

X Intercepts: (1, 0), Y Intercepts: (0, −5)

Asymptotes: لا يوجد

Extreme Points: لا يوجد

Interval Notation

Domain: (−∞ , ∞ )

Range: (−∞ , ∞ )

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Hyperbola Foci

For a right-left facing hyperbola, the Foci (focus points) are defined as (h+c, k), (h−c, k),
where c=√a²+b² is the distance from the center (h, k) to a focus

(h+c, k), (h−c, k)

Calculate Hyperbola properties

(x+3)²25 −(y−4)²9 =1: Right-left Hyperbola with (h, k)=(−3, 4), a=5, b=3

(−3+c, 4), (−3−c, 4)

Compute c:

c=√5²+3²: √34

(−3+√34, 4), (−3−√34, 4)

Solve instead

ddx ((4x³−x²+x−2)−(−x²+3))

parity 4x³−x²+x−2−(−x²+3)

symmetry 4x³−x²+x−2−(−x²+3)

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−▭▭	<	7	8	9	÷	`AC`
+▭▭	>	4	5	6	×	☐☐☐
×▭▭	(	1	2	3	−	`x`
▭ \|▭	)	.	0	=	+	`y`

nth term a_{n}=3^{n-1}

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