What is the range of y=1+5sec(4x) ?

The range of y=1+5sec(4x) is f(x) = 6

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range of y=1+5sec(4x)

range

y = 1 + 5 sec (4 x)

f (x) \leq - 4 or f (x) \geq 6

Interval Notation

(- \infty, - 4] \cup [6, \infty)

Solution steps

The range of the basic

sec

function is

sec (4 x) \leq - 1 or sec (4 x) \geq 1

sec (4 x) \leq - 1 or sec (4 x) \geq 1

Multiply the edges of the range by:

5

5 sec (4 x) \leq - 5 or 5 sec (4 x) \geq 5

Add to the edges of the range:

1

5 sec (4 x) + 1 \leq - 4 or 5 sec (4 x) + 1 \geq 6

Therefore the range is

f (x) \leq - 4 or f (x) \geq 6

\frac{1}{4} x - 3

f (x) = x^{2} - 4 x

4 x - 5 y = - 1

f (x) = 9 - 5 x

3 (\frac{x - 12}{3}) + 12

What is the range of y=1+5sec(4x) ?
The range of y=1+5sec(4x) is f(x)<=-4\lor f(x)>= 6