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(☐)^′	`ddx`	∂∂`x`	∫	∫_□^□	lim	∑	∞	`θ`	(`f` ◦ `g`)	`f`(`x`)

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simplify solve for inverse tangent line

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f(x)={

√`x`+2	`x`<1
`xx`²−6`x`+8	`x`≥ 1

Solution

Domain: −2≤ x<2 or 2<x<4 or x>4

X Intercepts: (−2, 0), Y Intercepts: (0, √2)

Asymptotes: Vertical x=2, x=4, Horizontal y=0

Monotone Intervals: Increasing:−2<x<1, Increasing:1<x<2, Increasing:2<x<2√2, Decreasing:2√2<x<4, Decreasing:4<x<∞

Interval Notation

Domain: [−2, 2)∪(2, 4)∪(4, ∞ )

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Solution steps

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Finding the scalar projection of ⃗ b onto ⃗ a : comp_⃗ a(⃗ b )=⃗ b ·⃗ a |⃗ a |

⃗ a =(

), ⃗ b =(

−8

)

|⃗ a |: |(

)|=√5

⃗ b · ⃗ a : (

−8

)(

)=−13

⃗ b · ⃗ a |⃗ a | =−13√5

Simplify

=−13√55

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√`x`+2	`x`<1
`xx`²−6`x`+8	`x`≥ 1

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

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