Which of the following describes the non-rigid transformation in the function shown below?
y-1=-(3x+1)^2

a. the graph is shifted 3 units down.
b. the graph is stretched vertically by a factor of 3.
c. the graph is reflected across the x-axis.
d. the graph is stretched horizontally to 1/3 the original width.

The graph is stretched horizontally to 1/3 the original width

For your best understanding I will brief all the transformations that you can infere from the expression.

Take as basis the graph y = x^2

When you multiply by a negative one you make a rigid translation (reflection across the x-axys)

When you add a positive constant to the total function (which is the same that substract it from the left side) you make a rigid translation, which is shifting a number of units equal to the value of the constant up.

When you add a positive constant to the argument of the function (this is the x before squaring it), you make a rigid traslation, which is shifting the graph a number of units equal to the value of the constant left.

When you multiply this function inside the argument, the graph is stretched vertically by a factor of the number square. In this case 3^2 = 9, but it squezes the function horizontally by a factor of 1/3.

Then, my option is the fourth of the list, because the function is shrinked horizontally by a factor of 1/3 (the term strecth is being used in a wide conception: if the factor is greater than 1 it is indeed a strecht but if the factor is less than 1 the stretch is a shrinkag).