Use the graph of logarithmic function f(x)
to answer the question.
A graph of an increasing log function that passes through (1, 0) and has a vertical asymptote at x equals 0.
What is the domain and range of the function?
Match the domain and range with the corresponding set of points.
Domain
Range
Options: (-∞,0) (0,∞) (-∞,∞) (1,∞) (0,1) (-∞,1)
Domain: (-∞,0)
Range: (1,∞)
Graph the function and identify the domain and range.
y equals negative 3 x squared
A. A coordinate plane with a parabola graphed. The parabola opens up with vertex at (0, 0). Domain is negative infinity to infinity; Range is 0 to infinity.
domain: (–∞, ∞)
range: [0, ∞)
B. A coordinate plane with a parabola graphed. The parabola opens down with vertex at (0, 0). Domain is negative infinity to infinity; Range is negative infinity 0.
domain: (–∞, ∞)
range: (–∞, 0]
C. A coordinate plane with a parabola graphed. The parabola opens down with vertex at (1, 0). Domain is negative infinity to infinity; Range is negative infinity 0.
domain: (–∞, ∞)
range: (–∞, 0]
D. A coordinate plane with a parabola graphed. The parabola opens down with vertex at (negative 1, 0). Domain is negative infinity to infinity; Range is 0 to infinity.
domain: (–∞, ∞)
range: [0, ∞)
B. A coordinate plane with a parabola graphed. The parabola opens down with vertex at (0, 0). Domain is negative infinity to infinity; Range is negative infinity 0.
domain: (–∞, ∞)
range: (–∞, 0]
To determine the domain and range of a logarithmic function, we need to consider its properties and the given information.
First, let's consider the domain. The domain of a logarithmic function is the set of all positive real numbers since the logarithm of a non-positive number is undefined.
From the given information, we know that the logarithmic function has a vertical asymptote at x = 0. This means that the function approaches negative infinity as x approaches 0 from the left side, and it approaches positive infinity as x approaches 0 from the right side. Hence, x = 0 is excluded from the domain.
Therefore, the domain of the logarithmic function is (-∞, 0) U (0, ∞).
Now let's consider the range. The range of a logarithmic function is the set of all real numbers, since the logarithm of any positive real number is defined.
The graph of the logarithmic function passes through the point (1, 0). This means that the function has a value of 0 when x = 1.
Hence, the range includes 0. Additionally, the range extends to positive and negative infinity on both sides. Therefore, the range of the logarithmic function is (-∞, ∞).
Matching the domain and range with the corresponding set of points, we have:
Domain: (-∞, 0) U (0, ∞)
Range: (-∞, ∞)
So the correct answer is:
Domain: (-∞, 0) U (0, ∞)
Range: (-∞, ∞)