Questions: Determine whether the graph is that of a function by using the vertical-line test. If it is, use the graph to find: (a) The domain and range (b) The intercepts, if any (c) Any symmetry with respect to the x-axis, the y-axis, or the origin (a) If the graph is that of a function, what are its domain and range? Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The domain is The range is (Type your answers in interval notation.) B. The graph is not a function. (b) If the graph is that of a function, what are its intercepts? Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The intercepts are (Type an ordered pair. Use a comma to separate answers as needed.) B. There are no intercepts.

Determine whether the graph is that of a function by using the vertical-line test. If it is, use the graph to find:
(a) The domain and range
(b) The intercepts, if any
(c) Any symmetry with respect to the x-axis, the y-axis, or the origin
(a) If the graph is that of a function, what are its domain and range? Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
A. The domain is The range is
(Type your answers in interval notation.)
B. The graph is not a function.
(b) If the graph is that of a function, what are its intercepts? Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
A. The intercepts are
(Type an ordered pair. Use a comma to separate answers as needed.)
B. There are no intercepts.

Transcript text: Determine whether the graph is that of a function by using the vertical-line test. If it is, use the graph to find: (a) The domain and range (b) The intercepts, if any (c) Any symmetry with respect to the $x$-axis, the $y$-axis, or the origin (a) If the graph is that of a function, what are its domain and range? Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The domain is $\square$ $\square$ The range is $\square$ (Type your answers in interval notation.) B. The graph is not a function. (b) If the graph is that of a function, what are its intercepts? Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The intercepts are $\square$ (Type an ordered pair. Use a comma to separate answers as needed.) B. There are no intercepts.

Solution

Solution Steps

Step 1: Determine if the graph is a function

To determine if the graph is a function, use the vertical line test. If any vertical line intersects the graph at more than one point, it is not a function. In this case, the graph passes the vertical line test, so it is a function.

Step 2: Find the domain and range

The domain of a function is the set of all possible input values (x-values). For this graph, the domain is all real numbers because the parabola extends infinitely in both directions along the x-axis. The range of a function is the set of all possible output values (y-values). For this graph, the lowest point is at y = -1, and it extends infinitely upwards. Therefore, the range is $ y \geq -1 $.

Step 3: Identify the intercepts

Intercepts are the points where the graph crosses the x-axis and y-axis. The graph crosses the y-axis at (0, -1) and the x-axis at (-1, 0) and (1, 0).