Question

for the graph of a function shown to the right, find (a) the domain and range (b) the intercepts, if any, and (c) the zeros, if any. (a) the domain of the graph is (type your answer in interval notation) the range of the graph is (type your answer in interval notation) (b) find the x-intercept(s). select the correct choice below and, if necessary, fill in the answer box to complete your choice. a. the x-intercept(s) is/are (13, 0) (type an ordered pair. use a comma to separate answers as needed) b. there is no x-intercept find the y-intercept(s). select the correct choice below and, if necessary, fill in the answer box to complete your choice. a. the y-intercept(s) is/are (0, 12) (type an ordered pair. use a comma to separate answers as needed) b. there is no y-intercept (c) determine the zeros of the function, if any. select the correct choice below and, if necessary, fill in the answer box to complete your choice. a. the zero(s) of the function is/are (type an integer or a decimal. use a comma to separate answers as needed) b. there is no zero of the function.

Explanation:

To solve this problem, we analyze the graph of the function:

Part (a): Domain and Range

• Domain: The domain of a function is the set of all possible \( x \)-values. From the graph, we can see that the function extends infinitely to the left and right, so the domain is all real numbers. In interval notation, this is \( (-\infty, \infty) \).
• Range: The range of a function is the set of all possible \( y \)-values. From the graph, we can see that the function extends infinitely upward and downward, so the range is also all real numbers. In interval notation, this is \( (-\infty, \infty) \).

Part (b): Intercepts

• x-intercept: The \( x \)-intercept is the point where the graph crosses the \( x \)-axis (where \( y = 0 \)). From the graph, this occurs at \( (3, 0) \).
• y-intercept: The \( y \)-intercept is the point where the graph crosses the \( y \)-axis (where \( x = 0 \)). From the graph, this occurs at \( (0, 12) \).

Part (c): Zeros of the Function

The zeros of a function are the \( x \)-values where \( y = 0 \) (the \( x \)-intercepts). From the graph, the zero is at \( x = 3 \).

Final Answers:

(a) Domain: \( (-\infty, \infty) \), Range: \( (-\infty, \infty) \)
(b) x-intercept: \( (3, 0) \), y-intercept: \( (0, 12) \)
(c) Zero: \( 3 \)

Answer:

To solve this problem, we analyze the graph of the function:

Part (a): Domain and Range

• Domain: The domain of a function is the set of all possible \( x \)-values. From the graph, we can see that the function extends infinitely to the left and right, so the domain is all real numbers. In interval notation, this is \( (-\infty, \infty) \).
• Range: The range of a function is the set of all possible \( y \)-values. From the graph, we can see that the function extends infinitely upward and downward, so the range is also all real numbers. In interval notation, this is \( (-\infty, \infty) \).

Part (b): Intercepts

• x-intercept: The \( x \)-intercept is the point where the graph crosses the \( x \)-axis (where \( y = 0 \)). From the graph, this occurs at \( (3, 0) \).
• y-intercept: The \( y \)-intercept is the point where the graph crosses the \( y \)-axis (where \( x = 0 \)). From the graph, this occurs at \( (0, 12) \).

Part (c): Zeros of the Function

The zeros of a function are the \( x \)-values where \( y = 0 \) (the \( x \)-intercepts). From the graph, the zero is at \( x = 3 \).

Final Answers:

(a) Domain: \( (-\infty, \infty) \), Range: \( (-\infty, \infty) \)
(b) x-intercept: \( (3, 0) \), y-intercept: \( (0, 12) \)
(c) Zero: \( 3 \)