What happens to the graph when you multiply f(x) by a negative constant?

When the function ( f(x) ) is multiplied by a negative constant, all y-values indeed become inverted. This inversion occurs because a negative multiplier reflects the points across the x-axis. For instance, if the original function produces a point at ( (x, y) ), after applying the negative constant, the corresponding point transforms to ( (x, -ky) ) where ( k ) is a positive constant. As a result, each y-value is inverted from positive to negative or vice versa, thereby creating a reflection of the graph across the x-axis.

The other options do not accurately describe the effect of multiplying by a negative constant. The graph does not shift horizontally to the left; horizontal shifts involve manipulating the input ( x ), not the output ( f(x) ). The graph does not become wider; this would imply a horizontal change in scale, which is not a result of multiplying y-values by a negative constant. Lastly, the graph does not stretch vertically; vertical stretching would require multiplying by a positive constant greater than one. Hence, multiplying by a negative constant specifically results in the inversion of all y-values.