Question

Need help asap please!

Answer 1

Answer:

$\textsf{ f(1) = \boxed{1} , meaning when a \boxed{1} is rolled on the die, the player is awarded}\\\\ \textsf{ \boxed{1} point. This interpretation \boxed{\sf makes \; sense} in the context of the problem.}$

$\textsf{ f(4.5) = \boxed{8} , meaning when a \boxed{4.5} is rolled on the die, the player is awarded} \\\\ \textsf{ \boxed{8} points. This interpretation \boxed{\sf does \; not \; make \; sense} in the context of the problem.}$

$\textsf{ f(10) = \boxed{19} , meaning when a \boxed{10} is rolled on the die, the player is awarded} \\\\ \textsf{ \boxed{19} points. This interpretation \boxed{\sf does \; not \; make \; sense} in the context of the problem.}$

$\textsf{Based on the observations above, it is clear that an appropriate domain for the}\\\\ \textsf{function is \boxed{ \{1, 2, 3, 4, 5, 6\}} .}$

Step-by-step explanation:

Given function:

$f(x)=2x-1$

where:

• x is the value rolled on the six-sided die.
• The sides of the die are labelled 1 to 6.

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f(1) means the value of the function when x = 1.  

Therefore, substitute x = 1 into the given function to find f(1):

$\begin{aligned}x=1 \implies f(1)&=2(1)-1\\&=2-1\\&=1\end{aligned}$

$\textsf{ f(1) = \boxed{1} , meaning when a \boxed{1} is rolled on the die, the player is awarded}\\\\ \textsf{ \boxed{1} point. This interpretation \boxed{\sf makes \; sense} in the context of the problem.}$

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f(4.5) means the value of the function when x = 4.5.

Therefore, substitute x = 4.5 into the given function to find f(4.5):

$\begin{aligned}x=4.5 \implies f(4.5)&=2(4.5)-1\\&=9-1\\&=8\end{aligned}$

As the faces of the six-sided die are labelled 1 to 6, the only values of x that make sense are 1, 2, 3, 4, 5 and 6.  Therefore, rolling a "4.5" does not make sense.

$\textsf{ f(4.5) = \boxed{8} , meaning when a \boxed{4.5} is rolled on the die, the player is awarded} \\\\ \textsf{ \boxed{8} points. This interpretation \boxed{\sf does \; not \; make \; sense} in the context of the problem.}$

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f(10) means the value of the function when x = 10.

Therefore, substitute x = 10 into the given function to find f(10):

$\begin{aligned}x=10 \implies f(1)&=2(10)-1\\&=20-1\\&=19\end{aligned}$

As the faces of the six-sided die are labelled 1 to 6, the only values of x that make sense are 1, 2, 3, 4, 5 and 6.  Therefore, rolling a "10" does not make sense.

$\textsf{ f(10) = \boxed{19} , meaning when a \boxed{10} is rolled on the die, the player is awarded} \\\\ \textsf{ \boxed{19} points. This interpretation \boxed{\sf does \; not \; make \; sense} in the context of the problem.}$

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The domain of a function is the set of all possible x-values.

As the faces of the six-sided die are labelled 1 to 6, the only possible values of x are 1, 2, 3, 4, 5 and 6.  

$\textsf{Based on the observations above, it is clear that an appropriate domain for the}\\\\ \textsf{function is \boxed{ \{1, 2, 3, 4, 5, 6\}} .}$

The domain can also be written as:

$\{x \in \mathbb{N} \; | \; 1 \leq x \leq 6 \}$  

or $\{x \in \mathbb{Z} \; | \; 1 \leq x \leq 6 \}$