The following table describes points on the graph of a function, f(x). What is the value of f(x) when x=400
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Step-by-step explanation:
2.4 Graphing the Basic Functions
LEARNING OBJECTIVES
Define and graph seven basic functions.
Define and graph piecewise functions.
Evaluate piecewise defined functions.
Define the greatest integer function.
Basic Functions
In this section we graph seven basic functions that will be used throughout this course. Each function is graphed by plotting points. Remember that f(x)=y and thus f(x) and y can be used interchangeably.
Any function of the form f(x)=c, where c is any real number, is called a constant function. Constant functions are linear and can be written f(x)=0x+c. In this form, it is clear that the slope is 0 and the y-intercept is (0,c). Evaluating any value for x, such as x = 2, will result in c.
The graph of a constant function is a horizontal line. The domain consists of all real numbers R and the range consists of the single value {c}.
We next define the identity function f(x)=x. Evaluating any value for x will result in that same value. For example, f(0)=0 and f(2)=2. The identity function is linear, f(x)=1x+0, with slope m=1 and y-intercept (0, 0).
The domain and range both consist of all real numbers.
The squaring function, defined by f(x)=x2, is the function obtained by squaring the values in the domain. For example, f(2)=(2)2=4 and f(−2)=(−2)2=4. The result of squaring nonzero values in the domain will always be positive.
The resulting curved graph is called a parabola. The domain consists of all real numbers R and the range consists of all y-values greater than or equal to zero [0,∞).
The cubing function, defined by f(x)=x3, raises all of the values in the domain to the third power. The results can be either positive, zero, or negative. For example, f(1)=(1)3=1, f(0)=(0)3=0, and f(−1)=(−1)3=−1.