Which Function Is Shown In The Graph Below?
In mathematics, a function is a relationship between two sets, such that each element of the first set is associated with exactly one element of the second set. Functions can be represented in many different ways, including by graphs, equations, and tables.
You are viewing: Which Function Is Shown In The Graph Below
One way to determine which function is shown in a graph is to look for the key features of the graph. These features can include the following:
- The shape of the graph: Some common shapes of graphs include lines, parabolas, and circles.
- The intercepts of the graph: The intercepts of a graph are the points where the graph crosses the x-axis or y-axis.
- The domain and range of the function: The domain of a function is the set of all possible values of x for which the function is defined. The range of a function is the set of all possible values of y for which the function is defined.
By looking at these key features, it is often possible to narrow down the possible functions that could be represented by the graph.
Example:
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The graph below shows a function that has the following features:
- The shape of the graph is a line.
- The intercepts of the graph are (0, 9) and (3, 1).
- The domain of the function is all real numbers.
- The range of the function is all real numbers greater than or equal to 1.
Based on these features, the possible functions that could be represented by the graph are:
- y = x + 9
- y = x^2 + 9
- y = 2x + 9
To determine the correct function, we can try to find the equation of the graph. We can do this by finding two points on the graph and using the point-slope form of the equation of a line.
We know that the graph passes through the points (0, 9) and (3, 1). Using these points, we get the following equation:
y – 1 = (1 – 9)(x – 3) y – 1 = -8(x – 3) y = -8x + 27
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Therefore, the correct function is y = -8x + 27.
Questions Related to Which Function Is Shown In The Graph Below:
- What is the domain of the function?
- What is the range of the function?
- What is the slope of the graph?
- What is the y-intercept of the graph?
- What is the equation of the graph in slope-intercept form?
- What is the equation of the graph in standard form?
These questions can be answered by analyzing the key features of the graph.
Conclusion
Determining which function is shown in a graph can be a challenging task, but it is often possible by looking for the key features of the graph. By understanding these features, it is possible to narrow down the possible functions and then find the correct function by using algebraic methods.
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Category: WHICH
