Question

Which of the following is true for the function f(x) = -2sin(x) - 3? 1) The maximum value of f(x) is -1 2) The minimum value of f(x) is -5 3) The graph of f(x) is a reflection of the graph of y = sin(x) about the x-axis 4) The y-intercept of f(x) is -3

Answer 1

Explanation:

sin(x) has a maximum of +1 and a minimum of -1.

therefore

2×sin(x) has a maximum of +2×+1 = +2 and a minimum of

+2×-1 = -2.

-2×sin(x) has a minimum of -2×+1 = -2 and a maximum of -2×-1 = +2. remember that a multiplication by -1 (or any negative number) flips the inequality sign.

-2×sin(x) - 3 has a minimum of -2 - 3 = -5 and a maximum of +2 - 3 = -1

so,

1) is true.

2) is true.

3) is false. the reflection of y = sin(x) about the x-axis would be simply y = -sin(x).

4) is true.

the y-intercept for any function is the functional value for x = 0 (that is actually the equation for the line that is the y-axis : all points, for which the x-coordinate = 0).

-2×sin(0) - 3 = -2×0 - 3 = 0 - 3 = -3