[tex]\sf{\underline{{Problem:}}}[/tex]
- f(W) = 5x + 7 is a one-to-one function
True or False
[tex]\sf{\underline{{Answer:}}}[/tex]
- True since the graph of a function f is known.
[tex]\sf{\underline{{Solution:}}}[/tex]
'The derivative of [tex] ax^n[/tex] is[tex] nax^{n-1} [/tex]so we will use that as a guide.
- [tex] f(w)=5x+7[/tex]
- [tex] 5x^{1-1} [/tex]
- [tex] 5x^{0} [/tex]
- [tex] 5\times 1 = 5 [/tex]
it is easy to determine if the function is 1 -to- 1 we'll use the Horizontal Line Test. If no horizontal line intersects the graph of the function f in more than one point, then the function is 1 to 1 .
Here are some sample points:
[tex] \begin{array}{c|c}\bold \purple{x} & \bold \purple{5.x+7} \\ \hline \\ - \infty & \sf Float ( - \infty ) \\ \hline \\ - \frac{7}{5} &0. \\ \hline \\ 1 &12. \\ \hline \\2 &17. \\ \hline \\ \infty& \sf Float ( - \infty )\\ \end{array}[/tex]
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