Question

One curve g of x is drawn with a dotted line and begins in quadrant 2 at approximately the point left parenthesis negative 1.75 comma 6 right parenthesis and descends in a convex fashion, inflecting and crossing the y-axis at the point left parenthesis 0 comma 1 right parenthesis, where it becomes concave and descends, crossing the x-axis at the point left parenthesis 1 comma 0 right parenthesis. It continues down into quadrant 3, ending at the point approximately left parenthesis 1.75 comma negative 6 right parenthesis. One curve f of x is drawn with a solid line and begins in quadrant 3 at approximately the point left parenthesis negative 1.75 comma negative 6 right parenthesis. It ascends and crosses the x-axis at the point left parenthesis negative 1 comma 0 right parenthesis. It continues upward and crosses the y-axis at the point left parenthesis 0 comma 1 right parenthesis, where it inflects and continues upward through quadrant 1 in a convex fashion to approximately the point left parenthesis 1.75 comma 6 right parenthesis.


The dotted graph is a reflection of the solid graph. The solid graph is a cubic function with the equation f(x)=x3+1
. Enter the option number that shows the equation of the image.

Option #1: g(x)=−x2+1

Option #2: g(x)=−x3−1

Option #3: g(x)=−x3+1

Option #4: g(x)=x3−1

(1 point)
The equation of the dotted graph is Option #

Answer 1

Option #3

Reason: The dotted graph is the reflection of f across the y-axis, so g(x)=f(−x) = (−x)^3+1 = −x^3+1.