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 slope of the function is $1.00. The y-intercept of the function is $60. The function can be represented by the equation y = y equals StartFraction 1 Over 10 EndFraction x plus 60.X + 60. The domain is all real numbers. The range is {y| y ≥ 60}.

The y-intercept is the value of y for which x = 0 (If no tokens are bought). In this case, that would be the single membership cost, which is $60. This statement is correct.

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

As previously mentioned, this equation is correct since it represents the membership cost plus the cost of each token multiplied by the number of tokens bought.

4. The domain is all real numbers

Real numbers include fractions and negative values, which cannot be a possible value for x. Therefore, the actual domain is all natural numbers (non-negative integers). This statement is incorrect.

5. The range is y ≥ 60

The range is all of the possible values of y. The minimum value is the cost of membership with no tokens ($60), and there is no maximum value since infinite tokens could be bought theoretically. This statement is correct.

AFOKE88 AFOKE88 · Answer 2 · 2021-11-19T17:40:10+01:00

The statements that 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 are;

B) The y-intercept of the function is $60

B) The y-intercept of the function is $60C) The function can be represented by the equation y = (1/10)x +60.

B) The y-intercept of the function is $60C) The function can be represented by the equation y = (1/10)x +60.E) The range is y ≥ 60

The equation of a line in slope intercept form is generally written as;

y = mx + c

Where;

m is slope

c is y-intercept

x is the input variable or domain

y is the output variable or range

Now, we are told that a single membership costs $60 per year. This is the price before any input which in this case game tokens are purchased.

Thus, it means the value of y-intercept is $60.

We are told that Game tokens can be purchased by members at the reduced rate of $1.00 per 10 tokens. This means;

y/x = 1/10

Thus, slope = 1/10

Now, writing the equation of this function in slope intercept form gives;

y = (1/10)x + 60

Now, the number of game tokens purchased cannot be less than 0. Thus;

Domain; x ≤ 0

Since x ≤ 0, then the cost can't be less than $60.

Thus; Range; y ≥ 60

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