What is the range of (3x+|x|)/x ?

The range of (3x+|x|)/x is f(x)=2\lor f(x)=4

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range of (3x+|x|)/x

range

\frac{3 x + ∣ x ∣}{x}

f (x) = 2 or f (x) = 4

Interval Notation

f (x) = 2 \cup f (x) = 4

Solution steps

Find the minimum and maximum value in each defined interval and unite the results

Domain of

\frac{3 x + ∣ x ∣}{x} : x < 0 or x > 0

Extreme Points of

\frac{3 x + ∣ x ∣}{x} :

None

Absolute value functions are piecewise functions

Find the function intervals:

x < 0, x > 0

Evaluate the function behavior for each interval

Find the range for the interval

- \infty < x < 0 : f (x) = 2

Find the range for the interval

0 < x < \infty : f (x) = 4

Combine the ranges of all domain intervals to obtain the function range

f (x) = 2 or f (x) = 4

f (x) = 2 or f (x) = 4

f (x) = 8 x^{2} + 9

f (x) = \frac{9}{x + 5}

f (x) = \frac{x ^{2}}{x ^{4} + 1}

f (x) = \frac{1}{e ^{x} + 1}

f (x) = (x - 1)^{2} - 2