Which of the following functions has the values of the range decrease as the values in the domain increase?f(x)= 2x − 15
f(x)= 2x − 15
f(x) = −2x + 15
f(x) = 12x − 15
f(x)= 15x − 2
f(x) = −2x + 15
To determine which of the given functions has the values of the range decrease as the values in the domain increase, we can look at the coefficients of the x-term.
In the first function, f(x) = 2x - 15, the coefficient of x is positive (2). This means that as the values of x increase, the values of f(x) will also increase. Therefore, the range does not decrease as the values in the domain increase.
In the second function, f(x) = -2x + 15, the coefficient of x is negative (-2). This indicates that as the values of x increase, the values of f(x) will decrease. Hence, the range decreases as the values in the domain increase.
In the third function, f(x) = 12x - 15, the coefficient of x is positive (12). Similar to the first function, this means that as the values of x increase, the values of f(x) will also increase. Thus, the range does not decrease as the values in the domain increase.
In the fourth function, f(x) = 15x - 2, the coefficient of x is positive (15). As mentioned earlier, this implies that as the values of x increase, the values of f(x) will increase as well. Consequently, the range does not decrease as the values in the domain increase.
Therefore, the only function where the values of the range decrease as the values in the domain increase is f(x) = -2x + 15.