Which of the following functions has the values of the range decrease as the values in the domain increase?
Responses
f(x)= 2x − 15
f(x)= 2x − 15
f(x)= 15x − 2
f(x)= 15x − 2
f(x) = −2x + 15
f(x) = −2x + 15
f(x) = 12x − 15
f(x) = −2x + 15
To determine which function has the values of the range decrease as the values in the domain increase, we need to examine the slope of each function.
A function with a positive slope indicates that the values in the range increase as the values in the domain increase. On the other hand, a function with a negative slope indicates that the values in the range decrease as the values in the domain increase.
Let's calculate the slopes for each function:
1. f(x) = 2x - 15
- The slope of this function is 2, which is positive.
2. f(x) = 15x - 2
- The slope of this function is 15, which is positive.
3. f(x) = -2x + 15
- The slope of this function is -2, which is negative.
4. f(x) = 12x - 15
- The slope of this function is 12, which is positive.
Based on the slopes, the only function that has a negative slope is f(x) = -2x + 15. Therefore, this is the function where the values of the range decrease as the values in the domain increase.