Home » Past Questions » Math » The table above shows some values of the linear function f. Which of the foll...

The table above shows some values of the linear function f. Which of the foll...


Question


The table above shows some values of the linear function f. Which of the following defines f ?

Options

A)
f(n) = n − 3
B)
f(n) = 2n − 4
C)
f(n) = 3n − 5
D)
f(n) = 4n − 6

The correct answer is C.

Explanation:

Choice C is correct. The graph of y = f(n) in the coordinate plane is a line that passes through each of the points given in the table. From the table, one can see that an increase of 1 unit in n results in an increase of 3 units in f(n); for example, f(2) - f(1) = 1 - (-2) = 3. Therefore, the graph of y = f(n) in the coordinate plane is a line with slope 3. Only choice C is a line with slope 3. The y-intercept of the line is the value of f(0). Since an increase of 1 unit in n results in an increase of 3 units in f(n), it follows that f(1) - f(0) = 3. Since f(1) = -2, it follows that f(0) = f(1) - 3 = -5. Therefore, the y-intercept of the graph of f(n) is -5, and the equation in slope-intercept form that defined f is f(n) = 3n - 5.

Choices A, B, and D are incorrect because each equation has the incorrect slope of the line (the y-intercept in each equation is also incorrect).


More Past Questions:


Discussion