Question

1-1 Additional Practice: Key Features of Functions. Need answers to these problems !!!

Answer 1

Answer:

1. Domain (-∞, ∞)

Range: (-20, ∞)

x-intercepts: (-5, 0), and (5, 0)

y-intercepts: (0, -25)

Interval positive: (-∞, -5), and (5, ∞)

Interval negative: (-5, 5)

Interval increasing: (0, ∞)

Interval decreasing: (-∞, 0)

Given that the shape is that of a quadratic graph, we have;

f(x) = (x - 5)×(x + 5) = x² - 25 = 0

Where;

The 5s are from the x-intercept

The slope = dy/dx = d(x² - 25)dx = 2·x

The slope at the point (-2, 0), therefore, x is -2, we have;

Slope = 2·x = 2 × x = 2 × (-2) = -4

The slope at the point (-2, 0) = -4

The rate of change over the interval = (-20 - (-25))/(-2 - 0) = -2.5

The rate of change over the interval = -2.5

2) Domain (-∞, ∞)

Range: (3, ∞)

x-intercepts: N/A

y-intercepts: (0, 7)

Interval positive: (-∞, ∞)

Interval negative: NA

Interval increasing: (-2, ∞)

Interval decreasing: (-∞, -2)

Given that the shape at (-2, 0) is that of a straight line graph, we have;

Rate of change = dy/dx = (7 - 3)/(0 - (-2)) = 2

The rate of change over the interval (-2, 0) = 2

3) Please find attached, the required graph drawn using Microsoft Excel

4) The key features are;

Domain: (0, 50/0.5) = (0, 100)

Range: (0, 50)

x-intercepts: (0, 0)

y-intercepts: (0, 0)

Interval positive: (0, 100)

Interval negative: N/A

Interval increasing: (0, 100)

Interval decreasing: N/A

The rate of change over the interval (-2, 0) = 0.5 ft³/min

Step-by-step explanation:

The domain is the range of values of the input (x) variables

The range is the range of values of the output (y) variables

The x-intercepts. are the points where the graph crosses the x-axis

The y-intercepts. are the points where the graph crosses the y-axis

The interval positive is the range of values over which the y-values are larger than 0

The interval negative is the range of values over which the y-values are lesser than 0

The interval increasing is the range of values over which the y-values are continuously increasing

The interval decreasing is the range of values over which the y-values are continuously decreasing

The rate of change over an interval is the ratio of the change in the y-values to the corresponding change in the x-values, over the range.