range of 2sin(2x)+3

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`x`²	`x`^□	log_□	√☐	^□√☐	≤	≥	□□	·	÷	`x`^◦	π
(☐)^′	`ddx`	∂∂`x`	∫	∫_□^□	lim	∑	∞	`θ`	(`f` ◦ `g`)	`f`(`x`)

☐²

x^☐

√☐

^□√☐

□□

log_□

θ

∞

∫

ddx

≥	≤	·	÷	`x`^◦	(☐)	\|☐\|	(`f` ◦ `g`)	`f`(`x`)	ln	`e`^☐
(☐)^′	∂∂`x`	∫_□^□	lim	∑	sin	cos	tan	cot	csc	sec

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range 2sin(2x)+3

Solution

1≤ f(x)≤ 5

Interval Notation

[1, 5]

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Solution steps

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Function range definition

The set of values of the dependent variable for which a function is defined

The range of the basic sin function is −1≤ sin(2x)≤ 1

−1≤ sin(2x)≤ 1

Multiply the edges of the range by: 2

−2≤ 2sin(2x)≤ 2

Add to the edges of the range: 3

1≤ 2sin(2x)+3≤ 5

Therefore the range is

1≤ f(x)≤ 5

Solve instead

domain 2sin(2x)+3

periodicity 2sin(2x)+3

amplitude 2sin(2x)+3

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