What is the range of-5cos(pi/4 x)-1 ?

The range of-5cos(pi/4 x)-1 is -6<= f(x)<= 4

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range of-5cos(pi/4 x)-1

range

- 5 cos (\frac{π}{4} x) - 1

- 6 \leq f (x) \leq 4

Interval Notation

[- 6, 4]

Solution steps

The range of the basic

cos

function is

- 1 \leq cos (\frac{π}{4} x) \leq 1

- 1 \leq cos (\frac{π}{4} x) \leq 1

Multiply the edges of the range by:

- 5

- 5 \leq - 5 cos (\frac{π}{4} x) \leq 5

Add to the edges of the range:

- 1

- 6 \leq - 5 cos (\frac{π}{4} x) - 1 \leq 4

Therefore the range is

- 6 \leq f (x) \leq 4

f (x) = \frac{7 x}{x - 8}

f (x) = x^{2} ∣ x ∣ + 9

f (x) = \frac{x ^{2} - x - 20}{x - 2}

\frac{x - 1}{2 x ^{2} - 15 x + 25}

f (x) = \frac{1}{x ^{2} + 5 x - 14}

What is the range of-5cos(pi/4 x)-1 ?
The range of-5cos(pi/4 x)-1 is -6<= f(x)<= 4