Questions: Use the horizontal line test to determine whether the function is one-to-one. Is the function one-to-one? Yes No f(x)=1-x^2

Solution Steps

The horizontal line test states that if any horizontal line intersects a function's graph more than once, then the function is not one-to-one. In this case, almost any horizontal line $y = k$ with $-4 \le k < 1$ intersects the graph of $f(x) = 1 - x^2$ twice. For example, the line $y=0$ intersects the graph at $x=-1$ and $x=1$.

Since horizontal lines intersect the graph more than once, the function $f(x) = 1 - x^2$ fails the horizontal line test.

Final Answer: No, the function is not one-to-one.