Question

1.(03.03 MC) The table below represents a linear function f(x) and the equation represents a function g(x).

X F(x) g(x) 5x +1
-1. -11
0. -1
1. 9
Part A: Write a sentence to compare the slope of the two functions and show the steps you used to determine the slope of f(x) and gx). (6 points)

Part B: Which function has a greater y-intercept? Justify your answer. (4 points) (10 points)

Answer 1

The linear function f(x) has a steeper slope (10) compared to g(x)'s slope (5), which is found by comparing the change in y over the change in x for f(x) and the coefficient of x for g(x). g(x) has a greater y-intercept (1) than f(x) (-1).

Step-by-step explanation:

To compare the slope of the linear functions f(x) and g(x), we need to find the slope of f(x) from the given table. The slope (m) is calculated as the change in y divided by the change in x which is (rise/run). Looking at the table for f(x), we can take the pair of points (0, -1) and (1, 9) to determine the slope:
m = ∆y/∆x = (9 - (-1))/(1 - 0) = 10/1 = 10.

For the function g(x) = 5x + 1, the slope is the coefficient of x, which is 5. Comparing the slopes, f(x) has a steeper slope of 10, while g(x) has a slope of 5.

For part B, the y-intercept is the constant term in the equation when x is 0. In g(x) = 5x + 1, the y-intercept is 1. The y-intercept of f(x) is -1 at x = 0 from the table. Therefore, g(x) has a greater y-intercept compared to f(x).

Answer 2

The slope of f(x) is 10 and the slope of g(x) is 5; g(x) has the greater y-intercept.

To find the slope of f(x), we use the slope formula: m=(y₂-y₁)/(x₂-x₁) = (-1--11)/(0--1) = (-1+11)/(0+1) = 10/1 = 10.

To find the slope of g(x), we just look at the form it is in. It is written in slope-intercept form, y=mx+b, where m is the slope. The number in g(x) that would correspond to m is 5.

The y-intercept of f(x) is found by looking at the points. Any y-intercept will have an x-coordinate of 0; the only point like this in the table is (0, -1) so the y-intercept is -1.

For g(x), we again look at the form y=mx+b. The number that corresponds with b is the y-intercept; in this case, it is 1. 1>-1, so g(x) has the larger y-intercept.