Question

How do I figure out b,c, and d

Answer 1

Answer:

  (b)  domain: (-∞, ∞)

  (c)  f(x) = 3 only at x=1

  (d)  range: (-∞, 3]

Step-by-step explanation:

(b) The domain is the horizontal extent of the region over which the function is defined. The function f(x) is defined for all x, from -∞ to +∞. The arrowheads on the ends of the graph mean the graph extends to infinity in x and y directions from those points (y goes to -∞, while x goes to ±∞).

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(c) Locate the horizontal grid line y=3 on the graph. Find all the points where it intersects the graph. There is only one: (1, 3). That is, x=1 is the only x-value for which f(x) = 3.

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(d) The range of the function is its vertical extent. The graph of f(x) extends from y = -∞ up to y = 3, so that is the range.

Answer 2

Step-by-step explanation:

From the graph:

a) f(3) = ?

The vertical line x = 3 intersect the parabola in the point (3, -1).

Therefore f(3) = -1

b) The domain: the set of all real numbers (R) ⇒ x ∈ (-∞, ∞)

c) f(x) = 3, x = ?

The horizonatal line y = 3 intersect the parabola in the point (1, 3) (vertex).

Therefore x = 1 (f(1) = 3.

d) The domain: y ≤ 3 ⇒ y ∈ (-∞, 3]