Find the Range f(x)=5cos(x)+1

Problem

ƒ(x)=5*cos(x)+1

Solution

1. Identify the range of the parent function cos(x) which is the set of all possible output values for the cosine function.

Range of *cos(x)=[−1,1]

2. Apply the inequality for the basic cosine function to represent its bounds.

−1≤cos(x)≤1

3. Multiply all parts of the inequality by the amplitude 5 to account for the vertical stretch.

−5≤5*cos(x)≤5

4. Add the constant 1 to all parts of the inequality to account for the vertical shift.

−5+1≤5*cos(x)+1≤5+1

5. Simplify the arithmetic to find the minimum and maximum values of the function.

−4≤ƒ(x)≤6

Final Answer

Range of *ƒ(x)=[−4,6]

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