30. What is the degree of the polynomial?
1 answer:
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Answer:
A) see attached for a graph. Range: (-∞, 7]
B) asymptotes: x = 1, y = -2, y = -1
C) (x → -∞, y → -2), (x → ∞, y → -1)
Step-by-step explanation:
<h3>Part A</h3>A graphing calculator is useful for graphing the function. We note that the part for x > 1 can be simplified:
This has a vertical asymptote at x=1, and a hole at x=2.
The function for x ≤ 1 is an ordinary exponential function, shifted left 1 unit and down 2 units. Its maximum value of 3^-2 = 7 is found at x=1.
The graph is attached.
The range of the function is (-∞, 7].
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<h3>Part B</h3>As we mentioned in Part A, there is a vertical asymptote at x = 1. This is where the denominator (x-1) is zero.
The exponential function has a horizontal asymptote of y = -2; the rational function has a horizontal asymptote of y = (-x/x) = -1. The horizontal asymptote of the exponential would ordinarily be y=0, but this function has been translated down 2 units.
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<h3>Part C</h3>The end behavior is defined by the horizontal asymptotes:
for x → -∞, y → -2
for x → ∞, y → -1
Answer: The answer is (b) (2, ∞)
Step-by-step explanation: We are given a function f(x) in the figure and we are to select out of the given options that accurately shows the range of the function defined.
Therefore, the range of the function f(x) will be greater then or equal to 2. So, the range will be [2, ∞).
Thus, the correct option is (b) (2, ∞).