Question

What is the minimum value for the function shown in the graph? Enter your answer in the box. A sinusoid function graphed on a coordinate plane. The horizontal x-axis ranges from negative 3 pi to 3 pi in increments of pi over 2. The vertical y-axis ranges from negative 7 to 1 in increments of 0.5. The function begins at begin ordered pair negative 3 pi comma negative 5.5 end ordered pair and increases in increments of pi over 2 until reaching begin ordered pair 3 pi comma negative 5.5 end ordered pair. The function begins at begin ordered pair negative 3 pi comma negative 5.5 end ordered pair and decreases to a minimum value of begin ordered pair negative 5 pi over 2 comma negative 6 end ordered pair. The graph then increases to a maximum value of begin ordered pair negative 3 pi over 2 comma negative 5 end ordered pair and decreases to a minimum value of begin ordered pair negative pi over 2 comma negative 6 end ordered pair. The graph then increases to a maximum value of begin ordered pair pi over 2 comma negative 5 end ordered pair and decreases to a minimum value of begin ordered pair 3 pi over 2 comma negative 6 end ordered pair. The graph then increases to a maximum value of begin ordered pair 5 pi over 2 comma negative 5 end ordered pair and decreases to a minimum value of begin ordered pair 3 pi comma negative 6 end ordered pair.

Answer 1

The sinusoidal function graph has a period of 2·π and a minimum point

with coordinates (-0.5·n·π, -6) where n = -5, -1, 3, ...

Response:

• The minimum value of the function is -6

How to find the minimum value of a function?

The minimum value of a function is the lowest vertex value of the

function.

The given graph description, is the graph of the following function;

f(t) = 0.5·sin(t) - 5.5

The minimum value is given at the location where, sin(t) = -1, which gives;

f(t) = 0.5 × (-1) - 5.5 = -6

The minimum value of the function is therefore;

• f(t) = -6

Learn more about the graphs of functions here:

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