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Martin is logging the number of strikes he bowls per hour. He has determined the function to be f(x) = 2x + 5, where x represents hours and f(x) represents the number of strikes he has bowled. Which of the following options describes the restrictions to the domain and range correctly?
Domain, nonnegative values; range, values greater than −2.5
Domain, nonnegative values; range, values greater than or equal to 5
Domain, nonnegative values; range, values less than −2.5
Domain, nonnegative values; range, values less than or equal to 5

Respuesta :

texaschic101
domain (x values) are non-negative values
range (f(x) values are : values greater then or equal to 5
luisaugustosc

Answer:

B. Domain, nonnegative values; range, values greater than or equal to 5

Step-by-step explanation:

Basically, domain is the set of values that x can take and range is the set of values that the result of f(x) can be.

Since x is the time Martin spends bowling, it cannot be negative. The least he can bowl is zero hours, so x cannot be a negative number.

For the lowest x can be (zero), f(x) is calculated as:

f(x) = 2(0)+5 = 0+5 = 5

For higher values of x, the equation can only yield higher results because the 2 that is multiplying it is positive. Multiplying a two positive numbers (2 and x, which cannot be negative) will always give a positive number. In other words, f(x) is directly proportional to x because its coefficient 2 is positive, which means that when x grows, f(x) grows.

This means that f(x) can never be lower than 5.

The best description is, then, nonnegative values for the domain and values greater or equal to 5 for the range.

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