Determine from its graph if the function is one-to-one.
-$$f ( x ) = \left\{ \begin{array} { l l }
8 x + 6 , & x

Question

Determine from its graph if the function is one-to-one.
-$$f ( x ) = \left\{ \begin{array} { l l } 
8 x + 6 , & x < 0 \
2 x ^ { 2 } - 5 , & x \geq 0
\end{array} \right.$$

Quizplus · Accepted Answer

The function is not one-to-one because the quadratic part $2x^2 - 5$ for $x \geq 0$ is not injective (one-to-one); it fails the horizontal line test since for any value of $y$ in the range of $2x^2 - 5$, there are two different $x$ values that map to it (except at the vertex of the parabola).

Determine from Its Graph If the Function Is One-To-One f(x)={8x+6,x<02x2−5,x≥0f ( x ) = \left\{ \begin{array} { l l } 8 x + 6 , & x < 0 \\2 x ^ { 2 } - 5 , & x \geq 0\end{array} \right.f(x)={8x+6,2x2−5,​x<0x≥0​

Determine from Its Graph If the Function Is One-To-One $f ( x ) = \left\{ \begin{array} { l l } 8 x + 6 , & x < 0 \\2 x ^ { 2 } - 5 , & x \geq 0\end{array} \right.$