Find the range of the function for the given domain.
f(x) = 4x - 7; {- 2, -1,0,1,2}
To find the range of the function, we need to find the set of all possible y-values that the function can output.
First, let's find the y-values for each x-value in the given domain:
For x = -2:
f(-2) = 4(-2) - 7 = -8 - 7 = -15
For x = -1:
f(-1) = 4(-1) - 7 = -4 - 7 = -11
For x = 0:
f(0) = 4(0) - 7 = 0 - 7 = -7
For x = 1:
f(1) = 4(1) - 7 = 4 - 7 = -3
For x = 2:
f(2) = 4(2) - 7 = 8 - 7 = 1
Therefore, the range of the function for the given domain {-2, -1, 0, 1, 2} is {-15, -11, -7, -3, 1}.
Find a reasonable domain and range for the function. Then graph the function.
A car can travel 31 mi for each gallon of gasoline. The function d(x) = 31x represents the distance d(x), in miles, that the car can travel with x gallons of gasonline. The car's fuel tank holds 18 gal.
A reasonable domain for this function would be the range of values that x (number of gallons of gasoline) can take. Since the car's fuel tank holds 18 gallons, it would make sense to have a domain of [0, 18]. This means that x can vary from 0 to 18 gallons of gasoline.
The range of this function would represent the distance in miles that the car can travel for each number of gallons of gasoline. Since the function is given as d(x) = 31x, the range would be the set of all possible values of d(x) for the values of x in the domain [0, 18]. The minimum possible value of d(x) would be 31*0 = 0 miles (when x = 0), and the maximum possible value of d(x) would be 31*18 = 558 miles (when x = 18).
To graph this function, we plot the points (x, d(x)) for some values of x within the domain [0, 18]:
(x, d(x))
(0, 0)
(6, 31*6 = 186)
(12, 31*12 = 372)
(18, 31*18 = 558)
Connecting these points, we get a diagonal line starting at the origin (0, 0) and going up to the point (18, 558). The x-axis represents the number of gallons of gasoline and the y-axis represents the distance in miles that the car can travel.
The graph of the function looks like this:
```
|
558| .-.
| .' '.
372| .' '.
| .' '.
186|.' '.
+------------------------------
0 6 12 18 (gallons)
```
Note: The graph is a straight line because the function is linear (d(x) = 31x).
To find the range of a function, we need to determine the set of all possible output values for the given inputs. In this case, we are given the function f(x) = 4x - 7 and the domain {-2, -1, 0, 1, 2}.
To find the range, we can substitute each value from the domain into the function and calculate the corresponding output value.
For x = -2: f(-2) = 4(-2) - 7 = -15
For x = -1: f(-1) = 4(-1) - 7 = -11
For x = 0: f(0) = 4(0) - 7 = -7
For x = 1: f(1) = 4(1) - 7 = -3
For x = 2: f(2) = 4(2) - 7 = 1
Therefore, the range of the function f(x) = 4x - 7 for the given domain {-2, -1, 0, 1, 2} is {-15, -11, -7, -3, 1}.