Question

Which of the following could be the equation of the function below?

On a coordinate plane, a curve crosses the y-axis at y = negative 3. It has a maximum at y = 1 and a minimum at y = negative 3. It goes through 1 cycle at pi.
y = negative 2 cosine (4 (x + pi)) minus 1
y = 2 cosine (x + pi) + 1
y = negative 2 cosine (2 (x + pi)) minus 1
y = 2 cosine (4 (x + pi)) + 2

Answer 1

C on E2020.

Explanation:

Answer 2

y = negative 2 cosine (2 (x + pi)) minus 1

Explanation:

The amplitude of the trig function will be half the difference of the minimum and maximum, so is ...

A = (1 -(-3))/2 = 2

The coefficient of x is 2π divided by the period, so is ...

B = (2π)/π = 2

The vertical offset is the average of the maximum and minimum:

C = (1 +(-3))/2 = -1

Since the extreme negative value is at x=0, this can be the opposite of the cosine function:

y = -A·cos(Bx) +C

The answer choices have a horizontal offset of pi, which does nothing, since the period is pi.

y = -2cos(2(x+π)) -1