Wendy is logging the number of video game levels she wins per hour. she has determined the function to be f(x) = 6x + 9, where x represents hours and f(x) represents the number of video game levels won. which of the following options describes the restrictions to the domain and range correctly?

a) domain, nonnegative values; range, values greater than −1.5
b) domain, nonnegative values; range, values less than −1.5
c) domain, nonnegative values; range, values greater than or equal to 9
d)domain, nonnegative values; range, values less than or equal to 9

Let

x--------> represents hours

f(x)------> represents the number of video game levels won

we know that

this is the equation of a line

The slope m is equal to

the domain is the interval-----------> [0, ∞)

the range is the interval--------> [9, ∞)

using a graph tool see the attached figure

therefore

the answer is the option

C) Domain, nonnegative values; range, values greater than or equal to 9

starting with:    

5 + x - 12 = 2x - 7   

5 + x - 12 - x = 2x - 7 - x (subtract x from both sides)   

5 - 12 = x - 7 (combine and cancel x's from both sides)   

5 - 12 + 7 = x - 7 + 7 (add 7 to both sides)   

0 = x (add numbers together on both sides)       

so in order for the equation to be true, x must be 0.   

trying x = -0.5   

5 + x - 12 = 2x - 7 (original equation)   

5 + -0.5 - 12 = 2(-0.5) - 7 (plug in value of x)   

5 + -0.5 - 12 = -1 - 7 (did multiplication)   

-7.5 = -8 (did addition on both sides)       

since -7.5 is obviously not equal to -8, the value of -0.5 for x is wrong.   

trying x = 0   

5 + x - 12 = 2x - 7 (original equation)   

5 + 0 - 12 = 2(0) - 7 (plug in value of x)   

5 + 0 - 12 = 0 - 7 (did multiplication)   

-7 = -7 (did addition on both sides)       

since -7 equals -7, that demonstrates that the value of 0 for x is correct.   

trying x = 1   

5 + x - 12 = 2x - 7 (original equation)   

5 + 1 - 12 = 2(1) - 7 (plug in value of x)   

5 + 1 - 12 = 2 - 7 (did multiplication)   

-6 = -5 (did addition on both sides)       

since -6 is obviously not equal to -5, the value of 1 for x is wrong.