Amelia is documenting the height of sunflower plants each week. She has determined the function to be f(x) = 3x + 3, where x represents time and f(x) represents the height of the plant. Which of the following options describes the restrictions to the domain (x) and range f(x) correctly?
A- range values greater than or equal to 3
B- range values greater than -1
C- range values less than -1
D- range values less than or equal to 3
I think it is A because you cannot have negative length so B and C cancel. Also, for 0 weeks when plugged in you get y=3. Therefore, it will increase from 3. I believe it is A, but no sure.
correct
You are correct! The correct answer is A. The function f(x) = 3x + 3 represents the height of the sunflower plants, where x represents time. Since the coefficient of x is positive (3), the function is linear and increases as x increases. Therefore, the range values of f(x) will be greater than or equal to the constant term (3), which eliminates options B and C. The range values cannot be less than or equal to 3 since the function increases, making option D incorrect. Thus, option A, which states that the range values are greater than or equal to 3, accurately represents the restrictions to the range (f(x)) for the given function.
You're on the right track!
To determine the restrictions on the domain (x) and the range (f(x)), let's analyze the function f(x) = 3x + 3.
For the domain (x), there appear to be no restrictions mentioned in the problem. Therefore, we can assume that x can take any value.
Now, let's determine the range (f(x)) values.
Since f(x) = 3x + 3, the function will output a value greater than or equal to 3 for any input value of x. This is because the coefficient of x is positive (3), which means the function will always increase as x increases. Additionally, when x = 0, we have f(0) = 3(0) + 3 = 3, which confirms that the function starts at a height of 3.
Therefore, the correct choice is A- range values greater than or equal to 3.