Question

Identify the statements which describe the graph of f (x) = 4()*+- 3. Select all that apply.

A) As x→ ∞o. f (x) → 0.
B) As x→-00, f (x) → ∞0.
C) The y-intercept is (0, -1).
D) The asymptote is y = -3.
E) The range is the set of real numbers.

Answer 1

The graph of f(x) = 4*x - 3 satisfies statements A, B, C, and E. It does not have a horizontal asymptote.

Step-by-step explanation:

The graph of the function f(x) = 4*x - 3 can be described by the following statements:

1. A) As x approaches positive infinity, f(x) approaches positive infinity. This means that as x gets larger and larger, the value of f(x) also increases without bound.
2. B) As x approaches negative infinity, f(x) approaches negative infinity. This means that as x gets smaller and smaller (approaching negative infinity), the value of f(x) also decreases without bound.
3. C) The y-intercept of the graph is (0, -3). This means that when x is 0, the value of f(x) is -3.
4. D) The graph does not have a horizontal asymptote y = -3. An asymptote is a line that the graph approaches but never reaches. In this case, there is no horizontal line that the graph gets infinitely close to.
5. E) The range of the function is the set of all real numbers. This means that for any real number y, there is a corresponding value of x that satisfies f(x) = y.