Question

A video game arcade offers a yearly membership with reduced rates for game play. A single membership costs $60 per year. Game tokens can be purchased by members at the reduced rate of $1.00 per 10 tokens.

Which statements represent the function of the yearly cost in dollars, y, based on x, the number of game tokens purchased for a member of the arcade? Select three answers.

The correct answers are: The y-intercept of the function is $60.
The function can be represented by the equation y = 1/10x+60.
and The range is {y| y ≥ 60}.

Answer 1

Let

x-------> the number of game tokens purchased for a member of the arcade

y-------> the function of the yearly cost in dollars

we know that

the function y of the yearly cost in dollars is equal to

$y = \frac{1}{10x} + 60$

This is the equation of the line

using a graph tool

see the attached figure

Statements

case a) The slope of the function is $1.00

The statement is False

The slope of the function is equal to

$\frac{1}{10} \frac{ dollar }{tokens}$

case b) The y-intercept of the function is $60

The statement is True

we know that

The y-intercept of the function is the value of the function when the value of x is equal to zero

so

for

$x = 0$

$y = \frac{1}{10} \times 0 + 60$

$y = 60$

case c) The function can be represented by the equation y =(1/10)x + 60

The statement is True

The equation of the function is equal to

$y = \frac{1}{10} x + 60$

case d) The domain is all real numbers

The statement is False

The value of x cannot be negative, therefore the domain is the interval

[0,∞)

case e) The range is {y| y ≥ 60}

The statement is True

The range of the function is the interval-------> [60,∞)

see the attached figure

Answer 2

Answer:

Let

x-------> the number of game tokens purchased for a member of the arcade

y-------> the function of the yearly cost in dollars

we know that

the function y of the yearly cost in dollars is equal to

y = \frac{1}{10x} + 60y=

10x

1

+60

This is the equation of the line

using a graph tool

see the attached figure

Statements

case a) The slope of the function is $1.00

The statement is False

The slope of the function is equal to

\frac{1}{10} \frac{ dollar }{tokens}

10

1

tokens

dollar

case b) The y-intercept of the function is $60

The statement is True

we know that

The y-intercept of the function is the value of the function when the value of x is equal to zero

so

for

x = 0x=0

y = \frac{1}{10} \times 0 + 60y=

10

1

×0+60

y = 60y=60

case c) The function can be represented by the equation y =(1/10)x + 60

The statement is True

The equation of the function is equal to

y = \frac{1}{10} x + 60y=

10

1

x+60

case d) The domain is all real numbers

The statement is False

The value of x cannot be negative, therefore the domain is the interval

[0,∞)

case e) The range is {y| y ≥ 60}

The statement is True

The range of the function is the interval-------> [60,∞)

see the attached figure