Question

For

the function pictured below. Fill in the following values.
a.Domain:
b. Range:
e increasing Interval:
d. Decreasing Interval:
e. Positive Interval(s]
f. Negative Interval (s:
g.Max:
h.min. i.Rate of Change (Slope) [2. 4]:

Answer 1

1. (-∞, ∞), [-4, ∞), (2, ∞), (-∞, 2), (-∞, 0) ∪ (4, ∞), (0, 4), DNE, -4, 2

2. y = -|x -4| -2

Explanation:

1.

a. the domain is the horizontal extent, (-∞, ∞)

b. the range is the vertical extent, [-4, ∞)

c. the function is increasing where it goes up to the right, (2, ∞)

d. the function is decreasing where it goes down to the right, (-∞, 2)

e. the function is positive where it is above the x-axis, (-∞, 0) ∪ (4, ∞)

f. the function is negative where it is below the x-axis, (0, 4)

g. the function extends to ∞, so has no maximum value

h. the vertex is the low point, or minimum value, -4

i. the function increases from -4 to 0 on the interval [2, 4] so has an average rate of change of (0 -(-4))/(4 -2) = 4/2 = 2

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2. Reflection across the x-axis negates every y-value. Multiply the given function by -1:

y = -|x-4| -2