Which Graph Shows a Function Where f(2) = 4?

When working with functions, it is important to be able to identify the graph that represents the function. In this article, we will discuss how to identify the graph of a function where f(2) = 4.

Understanding Functions

A function is a mathematical concept that relates an input value to an output value. The input value is called the independent variable, while the output value is called the dependent variable. In other words, the value of the dependent variable depends on the value of the independent variable.

Functions can be represented graphically, where the independent variable is plotted on the x-axis and the dependent variable is plotted on the y-axis. The resulting graph is a visual representation of the relationship between the two variables.

Identifying the Graph of a Function Where f(2) = 4

When we say that f(2) = 4, we mean that when the independent variable is 2, the dependent variable is 4. This information can help us identify the graph of the function.

One way to identify the graph is to use the point-slope form of the equation of a line. The point-slope form is y – y1 = m(x – x1), where (x1, y1) is a point on the line and m is the slope of the line.

In this case, we know that the point (2, 4) is on the line. We also know that the slope of the line is undefined, since the function is not linear. Therefore, we can conclude that the graph of the function is a vertical line passing through the point (2, 4).

Another way to identify the graph is to use the vertical line test. The vertical line test is a method used to determine if a graph represents a function. If a vertical line intersects the graph at more than one point, then the graph does not represent a function.

In this case, we can draw a vertical line passing through the point (2, 4). If the line intersects the graph at only one point, then the graph represents a function. If the line intersects the graph at more than one point, then the graph does not represent a function.

Therefore, we can conclude that the graph of the function where f(2) = 4 is a vertical line passing through the point (2, 4).

Conclusion

Identifying the graph of a function where f(2) = 4 can be done using the point-slope form of the equation of a line or the vertical line test. In this case, we determined that the graph is a vertical line passing through the point (2, 4).

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