For the reciprocal squared function [latex]f\left(x\right)=\frac{1}{{x}^{2}}[/latex], we cannot divide by [latex]0[/latex], so we must exclude [latex]0[/latex] from the domain. Select the correct choice below and, if … or ???x=2?? also written as ?? The vertical and horizontal asymptotes help us to find the domain and range of the function. The same applies to the vertical extent of the graph, so the domain and range include all real numbers. Now continue tracing the graph until you get to the point that is the farthest to the right. Models O y x If some vertical line intersects a graph in two or more points, the graph does not represent a function. Because the graph does not include any negative values for the range, the range is only nonnegative real numbers. Remember that domain is how far the graph goes from left to right. Let’s start with the domain. Graph each vertical line. Created in Excel, the line was physically drawn on the graph with the Shape Illustrator. If it is, use the graph to find (a) domain and range (b) the intercepts, if any. Note that the domain and range are always written from smaller to larger values, or from left to right for domain, and from the bottom of the graph to the top of the graph for range. The output quantity is “thousands of barrels of oil per day,” which we represent with the variable [latex]b[/latex] for barrels. I create online courses to help you rock your math class. ... (the change in x = 0), the result is a vertical line. The graph of a function f is a drawing that represents all the input-output pairs, (x, f(x)). A function is a correspondence between a first set, called the domain, and a second set, called the range, such that each member of the domain corresponds to exactly one member of the range. The blue N-shaped (inverted) curve is the graph of [latex]f(x)=-\frac{1}{12}x^3[/latex]. The ???x?? c) There is no vertical line that cuts the given graph at more than one point (see graph below) and therefore the relation graphed above is a function. What kind of test can be used . We can observe that the horizontal extent of the graph is –3 to 1, so the domain of [latex]f[/latex] is [latex]\left(-3,1\right][/latex]. The range of a function is always the y coordinate. We will now return to our set of toolkit functions to determine the domain and range of each. However, because absolute value is defined as a distance from 0, the output can only be greater than or equal to 0. So, to give you an example, please view Example 2 on the following page: https://www.algebra-class.com/vertical-line-test.html This is the graph of a quadratic function. ?1\leq y\leq 5??? The vertical line represents a value in the domain, and the number of intersections with the graph represent the number of values to which it corresponds. The given graph is a graph of a function because every vertical line that interests the graph in at most one point. Determine whether the graph below is that of a function by using the vertical-line test. The ???x?? For example, y=2x{1

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