What is the range of f(x)=((9(x-7)))/(|x-7|) ?

The range of f(x)=((9(x-7)))/(|x-7|) is f(x)=-9\lor f(x)=9

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range of f(x)=((9(x-7)))/(|x-7|)

range

f (x) = \frac{( 9 ( x - 7 ) )}{∣ x - 7 ∣}

f (x) = - 9 or f (x) = 9

Interval Notation

f (x) = - 9 \cup f (x) = 9

Solution steps

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

Domain of

\frac{9 ( x - 7 )}{∣ x - 7 ∣} : x < 7 or x > 7

Extreme Points of

\frac{9 ( x - 7 )}{∣ x - 7 ∣} :

None

Absolute value functions are piecewise functions

Find the function intervals:

x < 7, x > 7

Evaluate the function behavior for each interval

Find the range for the interval

- \infty < x < 7 : f (x) = - 9

Find the range for the interval

7 < x < \infty : f (x) = 9

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

f (x) = - 9 or f (x) = 9

f (x) = - 9 or f (x) = 9

4 x - 5 y = 0

\frac{6 - 3 x}{x - 10}

\frac{( x ^{2} + 3 x )}{( 3 x + 1 ) ^{2}}

3 x^{4} - 4 x^{3} - 12 x^{2} + 1

\frac{2 x}{x - 1}

What is the range of f(x)=((9(x-7)))/(|x-7|) ?
The range of f(x)=((9(x-7)))/(|x-7|) is f(x)=-9\lor f(x)=9