Some values of x and the corresponding values of f(x) are given in the table shown.

If there is a linear relationship between x and f(x), which of the following equations gives this relationship?

kx+ y = 1
y = -x² + k
In the system of equations above, k is a constant. When the equations are graphed in the xy-plane, the graphs intersect at exactly two points. Which of the following CANNOT be the value of k ?

$x minus 1 half a equals 0$
If x = 1 in the equation above, what is the value of a ?

(x − 6)² + (y + 5)² = 16
In the xy-plane, the graph of the equation above is a circle. Point P is on the circle and has coordinates (10, −5). If $top enclose P Q end enclose$ is a diameter of the circle, what are the coordinates of point Q ?

f (x) = x³ - 9x
g(x) = x² - 2x - 3
Which of the following expressions is equivalent to $fraction numerator f left parenthesis x right parenthesis over denominator g left parenthesis x right parenthesis end fraction comma text for end text x greater than 3$ ?

x

g(x)

-2

1

-1

2

0

3

1

4

2

5

3

6

4

7

The complete graph of the function f and a table of values for the function g are shown above. The maximum value of f is k. What is the value of g(k)?

Volume $equals fraction numerator 7 pi k cubed over denominator 48 end fraction$

The glass pictured above can hold a maximum volume of 473 cubic centimeters, which is approximately 16 fluid ounces.
Jenny has a pitcher that contains 1 gallon of water. How many times could Jenny completely fill the glass with 1 gallon of water? (1 gallon = 128 fluid ounces)

$K equals fraction numerator 200 v squared over denominator 2 end fraction$
In the equation above, the kinetic energy, K, of a 200-gram object is given in terms of its speed, v. If the equation is rewritten in the form v = $a square root of K$ , where a is a positive constant, what is the value of a ?

In the xy-plane, the point (p, r) lies on the line with equation y = x + b, where b is a constant. The point with coordinates (2p, 5r) lies on the line with equation y = 2x + b. If p ≠ 0, what is the value of $r over p$ ?

If we have coordinates of two points on a line, then we can use the slope formula to determine that line's slope. m = (y₂-y₁) / (x₂-x₁), or the ratio of the change in the y values and the x values, is the slope formula. 'x₁' and 'y₁' are the coordinates of the first point. The second points have the coordinates x₂ and y₂. If you have two points, you can always calculate the slope of a line. If you don't have access to two points, you can locate two points on the graph and use those to calculate the slope.
¶Observe the following helpful information:
- m = slope
¶-Rise = the difference between the y-values (y₂- y₁), where (x₁, y₁) = point 1 and (x₂, y₂) = point 2.
Run is equal to the difference between x-values (x₂ - x₁).

In the xy-plane, the point (p, r) lies on the line with equation y = x + b, where b is a constant. The point with coordinates (2p, 5r) lies on the line with equation y = 2x + b. If p ≠ 0, what is the value of $r over p$ ?

2, 10, 3, 7, 6
The mean of the list of numbers above is what fraction of the sum of the five numbers?

In the system of equation below, a and c are constant.
$1 half x plus 1 third y equals 1 over 6$
ax + y = 6
If the system of equation has an infinite number of solutions (x, y), what is the value of a?

The average annual energy cost for a certain home is $4,334. The homeowner plans to spend $25,000 to install a geothermal heating system. The homeowner estimates that the average annual energy cost will then be $2,712. Which of the following inequalities can be solved to find t, the number of years after installation at which the total amount of energy cost savings will exceed the installation cost?

The graph of the equation ax + ky = 6 is a line in the xy-plane, where a and k are constants. If the line contains the points (-2, -6) and (0, -3), what is the value of k?

Which of the following is an equivalent form of $cube root of f to the power of 6 a end exponent k squared end root$ , where f > 0 and k > 0?

f(x) = -500x² + 25,000x
The revenue f (x), in dollars, that a company receives from sales of a product is given by the function f above, where x is the unit price, in dollars, of the product. The graph of y = f (x) in the xy-plane intersects the x-axis at 0 and a. What does a represent?