Determine whether the graph is that of a function by using the vertical test. If

Question

Determine whether the graph is that of a function by using the vertical test. If it is, use the graph to find its domain and range. the intercepts, if any. any symmetry with respect to the x-axis, y-axis, or the origin. ls the graph that of a function? No Yes What are the domain and range of the function? Select the correct choice below and if necessary, fill in the answer box to complete your choice. The domain is The range is The graph is not that of a function. What are the intercepts of the function? Select the correct choice below and if necessary fill in the answer box to complete your choice. The intercept(s) is/are (Type an ordered pair. Use a comma to separate answers as needed.) The graph is not that of a function. if the graph is that of a function, determine what kinds of symmetry it has. Select all that apply. The graph is symmetrical with respect to the origin. The graph is symmetrical with respect to the x-axis. The graph is symmetrical with respect to the y-axis. The graph is not symmetrical. The graph is not that of a function.

Explanation / Answer

We know that the vertical line test determines in a visual way,whether curve is the graph of a function or not. A function of a single variable can only have one output, y, for each unique input, x. If a vertical line intersects a graph on an xy-plane more than once then for one value of x, then y has more than one value of for a value of x and hence the graph does not represent a function. If all vertical lines intersect a graph at most once, then the graph represents a function.

Here, the given graph appears to be that of a hyperbola, which is a function of two variables with an equation f(x,y) = x2/a2 –y2/b2 or, x2/a2 –y2/b2 = 1. Here, any values of x and y are valid inputs for f(x,y) as f(x.y) has been defined that way.Further, such a relation does not place any restrictions on what x or y could be. The relation is not a function of x, but is a function of x and y.

(a). The graph is that of a function of two variables viz. x and y. As per the vertical line test, it is not the function of x ( i.e. single variable). The domain of the function is(-5,-)U( 5,).The range is R, the set of all real numbers i.e. (-,)

(b) The x-intercepts are , where y = 0, i.e. -5 and 5.There is no y-intercept.

(c ) The X-Axis, the Y-Axis are both the lines of symmetry. The graph is also symmetric about the origin.

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