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Mathematics

1 answer:

Elena L [17]3 years ago

7 0

9514 1404 393

Answer:

(a) Function f is a proportion, so its slope is y/x = 3. The slope of function g is the x-coefficient, 7. The slope of function g is greater. (b) A proportion has a y-intercept of 0; function g has a y-intercept of 2. The y-intercept of function g is greater.
(a) The y-intercept is 665, the initial distance to destination. (b) The train's distance to destination is decreasing at 95 miles per hour. (c) The useful domain of the relation is 0 ≤ x ≤ 7.
(a) Standard form equation: 5x -y = -4. (We expect that "slope-intercept" form is desired: y=5x+4.) (b) f(x) = 5x +4. (c) The line can be graphed by starting at the y-intercept (0, 4) and drawing a line with slope 5. Axes will be labeled "Rental Time (hours)" (horizontal) and "Rental Cost (dollars)" (vertical). Axes can be numbered in units appropriate to the size of the graph.

Step-by-step explanation:

1. (a) The table contains the point (0, 0), and is said to represent a linear function. Consequently, we know that function f is a proportion. Its slope is ...

y/x = 3/1 = 3.

The slope of function g is the x-coefficient, 7. Since 7 > 3, the slope of function g is greater.

(b) As we said, function f has a y-intercept of 0. The y-intercept of function g is the constant in its equation, 2. Since 2 > 0, the y-intercept of function g is greater.

2. (a) The y-intercept is the value when x=0, which is 665. That is the train's initial distance to destination.

(b) The average rate of change from x = 1 to x = 4 is ...

m = (285 -570)/(4 -1) = -285/3 = -95 . . . . miles per hour

The train's distance to destination is decreasing at 95 miles per hour.

(c) From part B, we know the train covers 285 miles in 3 hours, so the time to destination will be 3 hours more than 4 hours. (Distance is 285 miles at 4 hours.) The useful domain of the relation is 0 ≤ x ≤ 7.

3. We can write the standard form equation using the relation ...

(y2 -y1)(x -x1) -(x2 -x1)(y -y1) = 0

(29 -14)(x -2) -(5 -2)(y -14) = 0 . . . . . fill in the given points: (2, 14), (5, 29)

15x -30 -3y +42 = 0 . . . . simpify

5x -y = -4 . . . . . divide by 3 and subtract 4

(We wonder if "slope-intercept" form is desired: y=5x+4.)

(b) The above equation can be solved for y (by adding y+4), and "y" replaced by "f(x)". The result is the "functional form" ...

f(x) = 5x +4

Axes will be labeled "Rental Time (hours)" (horizontal) and "Rental Cost (dollars)" (vertical).

Axes can be numbered in units appropriate to the size of the graph. (That will depend on the graph paper or tool used to create the graph.) An example of a graph is attached.