choose the correct graph.\n(b) the domain of the given function is (-∞, - 4)∪(-4,∞). (type your answer in…

choose the correct graph.\n(b) the domain of the given function is (-∞, - 4)∪(-4,∞). (type your answer in interval notation. use integers or fractions for any numbers in the expression.)\nthe range of the given function is (0,∞). (type your answer in interval notation. use integers or fractions for any numbers in the expression.)\n(c) what are the vertical asymptote(s)? select the correct choice and, if necessary, fill in the answer box(es) to complete your choice.\na. the left - vertical asymptote is ___. the right - vertical asymptote is ___. (type equations. use integers or fractions for any numbers in the equations.)\nb. there is one vertical asymptote. it is ___. (type an equation. use integers or fractions for any numbers in the equation.)\nc. there is no vertical asymptote.

choose the correct graph.\n(b) the domain of the given function is (-∞, - 4)∪(-4,∞). (type your answer in interval notation. use integers or fractions for any numbers in the expression.)\nthe range of the given function is (0,∞). (type your answer in interval notation. use integers or fractions for any numbers in the expression.)\n(c) what are the vertical asymptote(s)? select the correct choice and, if necessary, fill in the answer box(es) to complete your choice.\na. the left - vertical asymptote is ___. the right - vertical asymptote is ___. (type equations. use integers or fractions for any numbers in the equations.)\nb. there is one vertical asymptote. it is ___. (type an equation. use integers or fractions for any numbers in the equation.)\nc. there is no vertical asymptote.

Answer

Explanation:

Step1: Identify domain from graph

The domain is the set of all x - values for which the function is defined. Looking at the graph, the function is defined for all x - values except x = - 4. So the domain in interval notation is $(-\infty,-4)\cup(-4,\infty)$.

Step2: Identify range from graph

The range is the set of all y - values that the function can take. Since the range of the given function is stated as $(0,\infty)$, we note it down.

Step3: Identify vertical asymptotes

A vertical asymptote occurs where the function is undefined and the graph approaches infinity or negative infinity. From the graph, we see that x = - 4 makes the function undefined. So the vertical asymptote is x=-4.

Answer:

(b) Domain: $(-\infty,-4)\cup(-4,\infty)$ Range: $(0,\infty)$ (c) Left - vertical asymptote: x = - 4 Right - vertical asymptote: x = - 4