Decide whether the function is one-to-one. \[ y=4(x+1)^{2}-6 \] Is the given function one-to-one? Yes No

To determine if the function \( y=4(x+1)^{2}-6 \) is one-to-one, let's analyze its behavior. The function is a quadratic equation, specifically a parabola that opens upwards because of the positive coefficient in front of the squared term. Since parabolas are symmetric about their vertex, they will fail the horizontal line test, which means there will be at least one horizontal line that intersects the graph at two different points. Therefore, the function is not one-to-one. One common mistake when evaluating whether a function is one-to-one is assuming that all functions are one-to-one just because they are polynomials. Quadratic functions, like the one we're examining, often have this property. Visualizing the graph can help clarify this concept; if it looks like a "U," it's likely not one-to-one!