Given that a function, f(x), has a domain of -70 ≤ x ≤ -15 and a range of 30 ≤ f(x) ≤ 110 and that f(-60) = 80 and f(-17) = 40, select the statement that could be true for f(x).
A.
f(-60) = 95
B.
f(40) = -55
C.
f(-10) = 25
D.
f(-65) = 90
The statement that could be true for f(x) is C. f(-10) = 25.
This is because the given range is from 30 ≤ f(x) ≤ 110, and the point (f(-17) = 40) falls within this range. Therefore, it is possible for f(-10) to be 25.
To determine which statement could be true for f(x), we need to evaluate the statements based on the given domain and range of the function.
Given information:
Domain: -70 ≤ x ≤ -15
Range: 30 ≤ f(x) ≤ 110
Now let's evaluate each statement:
A. f(-60) = 95
Based on the given information, f(-60) = 80, not 95. Therefore, statement A is not true.
B. f(40) = -55
The domain of the function is -70 ≤ x ≤ -15, so f(40) is outside the domain. Therefore, statement B is not true.
C. f(-10) = 25
The domain of the function is -70 ≤ x ≤ -15, and f(-10) is within the domain. However, the range of the function is 30 ≤ f(x) ≤ 110, and 25 is not within this range. Therefore, statement C is not true.
D. f(-65) = 90
The domain of the function is -70 ≤ x ≤ -15, and f(-65) is within the domain. Additionally, the given information only provides the values of f(-60) and f(-17), which means we don't have any specific information about f(-65). Therefore, statement D could be true.
Therefore, the correct answer is D. f(-65) = 90.
To determine which statement could be true for the function f(x), we need to check if the given points (x, f(x)) lie within the given domain and range.
Given: Domain: -70 ≤ x ≤ -15
Range: 30 ≤ f(x) ≤ 110
Let's check the statements:
A. f(-60) = 95
Checking the point (-60, 95):
The x-value -60 lies within the given domain -70 ≤ x ≤ -15. However, the y-value 95 is not within the given range 30 ≤ f(x) ≤ 110. Therefore, statement A is not true for f(x).
B. f(40) = -55
Checking the point (40, -55):
The x-value 40 is outside the given domain -70 ≤ x ≤ -15. Therefore, statement B is not true for f(x).
C. f(-10) = 25
Checking the point (-10, 25):
The x-value -10 lies within the given domain -70 ≤ x ≤ -15. The y-value 25 lies within the given range 30 ≤ f(x) ≤ 110. Therefore, statement C could be true for f(x).
D. f(-65) = 90
Checking the point (-65, 90):
The x-value -65 lies within the given domain -70 ≤ x ≤ -15. The y-value 90 lies within the given range 30 ≤ f(x) ≤ 110. Therefore, statement D could be true for f(x).
Based on the analysis above, the statements C and D could be true for the function f(x). Therefore, the correct selection is:
C. f(-10) = 25
D. f(-65) = 90