(a) The domain of the function is (-∞; 0) U (0; +∞) and the range is (-∞; +∞).
(b) There are 2 x-intercepts: (-2, 0) and (2, 0). There is no y-intercept.
(c) This function does not have horizontal asymptotes.
(d) The vertical asymptote is x = 0.
(e) The oblique asymptote is y = -3x.
We want to find different elements of the function given in the graph.
(a) The domain and range of the function
- The domain of a function is the complete set of possible values of the independent variable. The domain of this function is (-∞; 0) U (0; +∞).
- The range of a function is the complete set of all possible resulting values of the dependent value. The range of this function is (-∞; +∞).
(b) The intercepts
The intercept is a point where the graph of a function intersects the axis. There are 2 x-intercepts: (-2, 0) and (2, 0). There is no y-intercept.
(c) Horizontal asymptotes
Horizontal asymptotes are horizontal lines that the graph of the function approaches as x tends to +∞ or −∞. This function does not have horizontal asymptotes.
(d) Vertical asymptotes
Vertical asymptotes are invisible vertical lines that certain functions approach, yet do not cross, when the function is graphed. The vertical asymptote is x = 0.
(e) Oblique asymptotes
An oblique asymptote is a slanted line that the function approaches as x approaches ∞ or -∞.
We have 2 points for this asymptote: (0, 0) and (2, -6). We can find its expression using the two-point form of a line.
y - y₁ = (y₂-y₁/x₂-x₁) (x - x₁)
y - 0 = (-6-0/2-0) (x - 0)
y = -3x
(a) The domain of the function is (-∞; 0) U (0; +∞) and the range is (-∞; +∞).
(b) There are 2 x-intercepts: (-2, 0) and (2, 0). There is no y-intercept.
(c) This function does not have horizontal asymptotes.
(d) The vertical asymptote is x = 0.
(e) The oblique asymptote is y = -3x.
Learn more about asymptotes here: https://brainly.com/question/4930698
