Provide an appropriate response.
-If $\mathrm { f } ( \mathrm { x } )$ is one-to-one, can anything be said about $h ( x ) = 6 f ( x ) + 3$ ? Is it also one-to-one? Give reasons for your answer.
A) Yes, $h ( x )$ will be one-to-one. For every distinct value of $f ( x )$ there is one distinct value of $h ( x )$.
B) No, $h ( x )$ will not be one-to-one. The function $h ( x )$ assumes the same value for at least two different $f ( x )$-values.
C) Yes, $h ( x )$ will be one-to-one. The inverse of $f ( x )$ is $h ( x )$ and is therefore one-to-one.
D) No, $h ( x )$ will not be one-to-one. The function $h ( x )$ does not pass the horizontal line test.

Question

Quizplus · Accepted Answer

If $f(x)$ is one-to-one, then for every distinct $x$, there is a distinct $f(x)$. Multiplying $f(x)$ by 6 and adding 3 (to get $h(x) = 6f(x) + 3$) does not change the one-to-one nature of the function, because the transformation is linear and preserves the uniqueness of each output.

Provide an Appropriate Response f(x)\mathrm { f } ( \mathrm { x } )f(x)

Provide an Appropriate Response $\mathrm { f } ( \mathrm { x } )$