1.
Evaluate f(6) for {(0,6), (3, 12), (6, 54), (2,6)}
Correct Answer
D. 54
Explanation
The given set of points represents a function where the x-coordinate corresponds to the input and the y-coordinate corresponds to the output. By looking at the set of points, we can see that when x=6, the corresponding y-value is 54. Therefore, when evaluating f(6), the output is 54.
2.
A squirrel drops a nut from tree limb. The nut’s height, in metres, after t seconds is modeled by the function –4.9t + 12. About when does the nut hit the ground?
Correct Answer
C. Between 1.5 and 1.6 seconds
Explanation
The nut hits the ground when its height is equal to 0. To find the time when this occurs, we set the function -4.9t + 12 equal to 0 and solve for t. By solving the equation, we find that t is approximately 1.551 seconds. Therefore, the nut hits the ground between 1.5 and 1.6 seconds.
3.
The graph of y = f(x) is shown. Evaluate f(2)
Correct Answer
D. 5
4.
A car salesman is paid a commission based on the function f(p) = –0.002p + 100 where p is the sale price of a vehicle. How much will be earn from a car that sells for $15000?
Correct Answer
C. 400
Explanation
The car salesman is paid a commission based on the function f(p) = –0.002p + 100, where p is the sale price of a vehicle. To find out how much he will earn from a car that sells for $15000, we substitute p = 15000 into the function. f(15000) = –0.002(15000) + 100 = -30 + 100 = 70. Therefore, the car salesman will earn $70 from a car that sells for $15000. However, none of the given answer choices match this calculation, so the correct answer is not available.
5.
A function g is defined by g(x)= x^2 – 9x + 18. Evaluate g(2n)
Correct Answer
C. 4n^2 – 36n + 18
Explanation
The given function g(x) is defined as g(x) = x^2 - 9x + 18. To evaluate g(2n), we substitute 2n in place of x in the function.
g(2n) = (2n)^2 - 9(2n) + 18
= 4n^2 - 18n + 18
Therefore, the correct answer is 4n^2 - 18n + 18.
6.
The relation between the selling price of a toothbrush and revenue, r(s) is represented by the function r(s) = –5s^2 + 20s + 25 and its graph above
If r(s) = 45, what is the selling price, s?
Correct Answer
C. $2
Explanation
The given equation represents the revenue, r(s), as a function of the selling price, s, of a toothbrush. The equation is r(s) = –5s^2 + 20s + 25. To find the selling price when the revenue is 45, we set r(s) equal to 45 and solve for s.
45 = –5s^2 + 20s + 25
Subtracting 45 from both sides, we get
0 = –5s^2 + 20s - 20
Dividing through by -5, we have
0 = s^2 - 4s + 4
Factoring the quadratic equation, we get
0 = (s - 2)(s - 2)
This gives us the solution s = 2. Therefore, the selling price is $2.
7.
If the point (–2,–3) is on the graph of y=f(x), what is the value of f(–2)?
Correct Answer
A. –3
Explanation
Since the point (-2,-3) lies on the graph of y=f(x), it means that when x=-2, y=-3. Therefore, the value of f(-2) is -3.
8.
For a function f(5) = –1, what does f(5) represent?
Correct Answer
B. The y–coordinate of the point
Explanation
The given function f(5) = -1 represents the y-coordinate of the point. In a function, the value of f(x) represents the y-coordinate of the point on the graph of the function when x is equal to the given value. In this case, when x is equal to 5, the y-coordinate is -1. Therefore, f(5) represents the y-coordinate of the point.
9.
The sum of two whole numbers is 16. Their product can be modeled by the function g(x) = x(16–x). What is the largest product?
Correct Answer
D. 64
Explanation
The function g(x) = x(16-x) represents the product of two whole numbers whose sum is 16. To find the largest product, we need to find the maximum value of the function. By analyzing the function, we can see that the product is maximized when x is equal to half of the sum (16/2 = 8). Plugging in x=8 into the function, we get g(8) = 8(16-8) = 8(8) = 64. Therefore, the largest product is 64.
10.
Evaluate f(x) = –3x + 7 if x = – 2
Correct Answer
D. 13
Explanation
By substituting x = -2 into the given function f(x) = -3x + 7, we can evaluate the expression. Plugging in -2 for x, we have -3(-2) + 7. Simplifying this, we get 6 + 7 = 13. Therefore, the value of f(x) when x = -2 is 13.