a. The domain of the function is x. The range of the function is y.
b. The intercepts of the function are;
x-intercept: x = 0.
y-intercept: y = 0.
c. The horizontal asymptote is y = -4.
d. The vertical asymptote is x = -2.
e. There are no oblique asymptotes.
A range is the set of all real numbers that connects with the elements of a domain for any function, usually read from bottom to top.
A domain is the set of all real numbers (x-values) for which a particular relation or function is defined.
Part a.
By critically observing the graph of this rational function, we have the following domain (x-values from left to right) and range (y-values from bottom to top):
Domain = x.
Range = (y.
Part b.
The intercept of a graph is the point where the graph of a line crosses either the x-axis or the y-axis on a coordinate plane. Based on the graph, the intercepts are as follows;
x-intercept: x = 0.
y-intercept: y = 0.
Part c.
A horizontal asymptote is a horizontal line (y = b) where the graph of a function approaches the line as the input values approach negative infinity (-∞) to positive infinity (∞);
Horizontal asymptote is y = -4.
Part d.
A vertical asymptote of a function refers to the value of x which makes its denominator equal to zero (0);
Vertical asymptote is x = -2.
Part e.
An oblique asymptote is also known as slant asymptote and it refers to an asymptote along a slanted line that a function approaches as x approaches ∞ or -∞. Based on the graph, there are no oblique asymptotes.