1.
Which of the following represents the domain of the function ?
Correct Answer
C.
2.
Table A
x
5
6
7
4
9
y
-9
-5
-7
6
4
Table B
x
4
7
3
15
8
y
-4
-1
4
3
3
Usa Table B to find y = f(4).
Correct Answer
A. -4
Explanation
Looking at Table B, we can see that when x = 4, y = -4. Therefore, the value of y when x = 4 is -4.
3.
Does describe y as a function of x?
Correct Answer
A. True
Explanation
The given correct answer is true because the question is asking if y is described as a function of x. If y is described as a function of x, it means that for every value of x, there is a unique value of y. This implies that there is a clear relationship between x and y, where the value of y depends on the value of x. Therefore, the statement "Does describe y as a function of x?" is true.
4.
Table A
x
5
6
7
4
9
y
4
-5
-7
6
4
Table B
x
4
7
3
15
8
y
-4
-1
4
3
3
Does Table A describe x as function of y?
Correct Answer
B. No
Explanation
Table A does not describe x as a function of y because for the value of y=4, there are two different corresponding values of x (5 and 9). In a function, each input (y) should have only one unique output (x), but in this case, there is a repetition of the input value y=4. Therefore, Table A does not satisfy the criteria for a function.
5.
One line passes through the points (-12, 16) and (-1, 38), and a second line has equation 2y + x = 23. Are the line parallel, perpendicular, or neither?
Correct Answer
B. Perpendicular
Explanation
The two lines are perpendicular because the product of their slopes is -1. The slope of the first line can be found using the formula (y2 - y1) / (x2 - x1), which gives (38 - 16) / (-1 - (-12)) = 22/11 = 2. The slope of the second line can be found by rearranging the equation 2y + x = 23 to y = -(1/2)x + 23/2, which has a slope of -1/2. The product of the slopes (-1/2) * 2 = -1, indicating that the lines are perpendicular.
6.
Which of the following represents the domain of the function ?
Correct Answer
B.
7.
Write the equation that passes through (5, -3) and is parallel to the line with equation 2x + y = -3.
Correct Answer
y = -2x + 7
y=-2x+7
y = -2x+7
y = -2x+7
Explanation
Don't forget that your answer should say "y = ...."
8.
For the function , compute the average rate of change between x = -1 and x = 2.
Correct Answer
3
m = 3
Explanation
The average rate of change between x = -1 and x = 2 is determined by finding the difference in the function values at these two points and dividing it by the difference in the x-values. In this case, the function value is constant at 3 for all x-values, so the average rate of change is also constant and equal to 3.
9.
The average salary of a classroom teacher in the United States is given by f(t) = 982.06t + 32,903.77, where t is the number of years from 1990. What was the average salary in 2000?
Correct Answer
42724.37
$42724.37
$42,724.37
f(x) = 42, 724.37
f(x) = 42724.37
Explanation
The given function f(t) represents the average salary of a classroom teacher in the United States based on the number of years from 1990. To find the average salary in 2000, we need to substitute t = 10 (since 2000 is 10 years after 1990) into the function.
f(t) = 982.06t + 32,903.77
f(10) = 982.06(10) + 32,903.77
f(10) = 9,820.6 + 32,903.77
f(10) = 42,724.37
Therefore, the average salary in 2000 is $42,724.37.
10.
The equation of the line that fits the data points in the table is f(a) = 0.017924A + 0.01. Use the equation to find f(28000).
Correct Answer
501.882
501.88
f(a) = 501.882
f(a)=501.882
Explanation
The given equation f(a) = 0.017924A + 0.01 represents a linear relationship between the variable a and the function f(a). To find f(28000), we substitute 28000 for A in the equation and solve for f(a). Therefore, f(28000) = 0.017924(28000) + 0.01 = 501.882.
11.
A company has revenue given by R(x) =564x dollars and total cost given by C(x) = 40,000 + 64x dollars, where x is the number of units poroduced and sold. Write the profit function.
Correct Answer
P(x) = 500x - 40000
P(x)=500x-40000
P(x) = 500x - 40,000
Explanation
Remember P(x) = R(x) - C(X). Your answer should be in simplest form.
12.
For the function , find .
Correct Answer
10
13.
A company has determined that its profit for product can be described by a linear function. The profit from the production and sale of 150 units is $455, and the profit from 250 units is $895. Write the equation of the profit function P(x) for this product.
Correct Answer
P(x) = 4.4x - 205
P(x)=4.4x-205
Explanation
Remember P(x) = R(x) - C(X). Your answer should be in simplest form.
14.
Whice of the following equations is the point-slope form for a linear equation?
Correct Answer
C.
Explanation
The correct answer is "y = mx + b". This equation is in the point-slope form for a linear equation, where "m" represents the slope of the line and "b" represents the y-intercept. This form allows us to easily identify the slope and y-intercept of the line by comparing the equation to the standard form, y = mx + c.
15.
Which of the following graphs represents the function ?
Correct Answer
B.