1. What is the domain of the function f(x) given its graph below?
A. (−∞, ∞)
B. [2, ∞)
C. [-2, ∞)
D. (−∞, 2]
C. [-2, ∞)
To determine the domain of a function from its graph, we need to look at the x-values that are covered by the graph.
Looking at the graph provided, we can see that it starts at x = -2 and continues to the right without any breaks or interruptions. Therefore, the x-values covered by the graph are all values greater than or equal to -2.
Thus, the correct answer is: C. [-2, ∞)
To determine the domain of the function f(x) based on its graph, we need to look at the values of x for which the graph is defined.
Looking at the graph provided, we can see that the graph starts at x = -2 and continues indefinitely to the right. This means that the function is defined for all x-values greater than or equal to -2.
Therefore, the correct answer is option C. [-2, ∞), which represents all the x-values from -2 to positive infinity.
1. What is the average rate of change of the function described by the table below over the interval [−2,1] ?
X -3 -2 -1 0 1 2 3
F(x) -14 -7 -2 1 2 1 -2
A. -3
B. 9
C. 3
D. -9
2. What is the average rate of change of the function described by the table below over the interval [−1,3] ?
X F(x)
-3 -2
-2 -4
-1 -2
0 4
1 14
2 28
3 46
3. Given the following graph, find the average rate of change on the interval [−1, 2]
A. 0
B. 1/3
C. 3
D. -2
4. What is the average rate of change of f(x)=4x^2−2x+3 over the interval [−2, 2] ?
A. 2
B. 8
C. -8
D. -2
5. What is the average rate of change of f(x)=4x^2−2x+3 over the interval [−2, 2] ?
A. 8
B. 4
C. -8
D. -4
1. To find the average rate of change over the interval [-2,1], we need to calculate the difference in the values of f(x) at the endpoints of the interval and divide by the difference in the x-values.
The value of f(x) at x = -2 is -7 and at x = 1 is 2. The difference in the values is 2 - (-7) = 9.
The difference in the x-values is 1 - (-2) = 3.
Therefore, the average rate of change is 9/3 = 3.
The correct answer is C. 3.
2. To find the average rate of change over the interval [-1,3], we need to calculate the difference in the values of f(x) at the endpoints of the interval and divide by the difference in the x-values.
The value of f(x) at x = -1 is -2 and at x = 3 is 46. The difference in the values is 46 - (-2) = 48.
The difference in the x-values is 3 - (-1) = 4.
Therefore, the average rate of change is 48/4 = 12.
3. From the graph, we can see that the y-value at x = -1 is 2 and at x = 2 is 6.
The difference in the y-values is 6 - 2 = 4.
The difference in the x-values is 2 - (-1) = 3.
Therefore, the average rate of change is 4/3.
The correct answer is B. 1/3.
4. To find the average rate of change of f(x) = 4x^2 - 2x + 3 over the interval [-2,2], we need to calculate the difference in the values of f(x) at the endpoints of the interval and divide by the difference in the x-values.
The value of f(x) at x = -2 is 24 and at x = 2 is 20. The difference in the values is 20 - 24 = -4.
The difference in the x-values is 2 - (-2) = 4.
Therefore, the average rate of change is -4/4 = -1.
The correct answer is D. -2.
5. To find the average rate of change of f(x) = 4x^2 - 2x + 3 over the interval [-2,2], we need to calculate the difference in the values of f(x) at the endpoints of the interval and divide by the difference in the x-values.
The value of f(x) at x = -2 is 24 and at x = 2 is 20. The difference in the values is 20 - 24 = -4.
The difference in the x-values is 2 - (-2) = 4.
Therefore, the average rate of change is -4/4 = -1.
The correct answer is D. -4.