A sinusoidal function whose frequency is 3, maximum value is 12, minimum value is −6 has a y-intercept of 3.

Which function could be the function described?

1.) g(x) = 2x - 14

2.) g(x) = 2x - 10

3.) g(x) = 8x + 24

4.) g(x) = 8x - 6

Step-by-step explanation:

You are given a function

F(x) = 2x - 6

1.) When a function shift to the left along x axis, you will add. But if it shifts right, you will subtract. Therefore

g(x) = 2(x - 4) - 6

Open the bracket

g(x) = 2x - 8 - 6

g(x) = 2x - 14

2.) Translation or shifting at y axis is vice versa of translation at x axis. Up is positive, down is negative. Therefore,

g(x) = 2x - 6 -4

g(x) = 2x - 10

3.) Compression of 1/4 along y axis will be the reciprocal of the value multiply by the function. The compressed function will be

g(x) = 4( 2x - 6 )

Open the bracket

g(x) = 8x + 24

4.) When you stretch along x axis, you will only multiply the value by coefficient of x. The stretch function along x axis will be

g(x) = (4) 2x - 6

g(x) = 8x - 6