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Finding the Domain & Range from the Graph of a Continuous Function
Step 1 : To find the domain of the function, look at the graph, and determine the largest interval of { equivalent } x { /eq } -values for which there is a graph above, below, or on the { equivalent } x { /eq } -axis. In early words, the knowledge domain is the fit of all the { equivalent } x { /eq } -coordinates of the points on the graph. Express the knowledge domain either in interval notation or as an inequality involving { equivalent } x { /eq } ( or whatever the independent variable is ) .
Step 2 : To find the stove of the function, look at the graph, and determine the largest interval of { equivalent } y { /eq } -values for which there is a graph to the leave of, to the correct of, or on the { equivalent } y { /eq } -axis. In other words, the range is the set of all the { equivalent } y { /eq } -coordinates of points on the graph. Express the range either in interval notation or as an inequality involving { equivalent } y { /eq } ( or whatever the subject variable is ) .
Finding the Domain & Range from the Graph of a Continuous Function: Vocabulary
Domain of a function : The knowledge domain of a function, { equivalent } f { /eq }, is the set of values, { equivalent } x { /eq }, for which { equivalent } f ( x ) { /eq } is define. In other words, the world of { equivalent } f { /eq } is the set of valid inputs of { equivalent } f { /eq }. Graphically speak, the domain is the adjust of all { equivalent } x { /eq }, such that { eq } ( x, y ) { /eq } is a point on the graph of { equivalent } f { /eq } .
Range of a function : The range of a function, { equivalent } f { /eq }, is the set of all values, { equivalent } farad ( x ) { /eq }, such that { eq } x { /eq } is in the domain of { equivalent } f { /eq }. In early words, the range of { equivalent } f { /eq } is the plant of outputs of { equivalent } f { /eq }. Graphically speaking, the range is the set of all { equivalent } y { /eq } such that { eq } ( x, y ) { /eq } is a point on the graph of { equivalent } f { /eq } .
Continuous function : A function whose graph has no gaps within its domain .
now let ‘s use these steps and definitions to practice finding the domain and range of continuous functions given their graph with two distinctive examples .
Finding the Domain & Range from the Graph of a Continuous Function: Example 1
Use the graph of { equivalent } f { /eq } below to determine the sphere and range of { equivalent } f { /eq } .
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Step 1 : Focusing on the { equivalent } x { /eq } -axis first, we see that the largest time interval of { equivalent } x { /eq } -values for which there is a graph above, below, or on the { equivalent } x { /eq } -axis is the time interval from x = -2 to x = 2, not including 2. The value 2 is not included, because the open circle at { equivalent } x=2 { /eq } indicates that this target is not included in the graph of { equivalent } f { /eq }. frankincense, there is no target on the graph with an { equivalent } x { /eq } -coordinate of 2. consequently, the sphere of { equivalent } f { /eq } is the interval { equivalent } [ -2,2 ) { /eq }. Equivalently, the sphere is { equivalent } -2\le x < 2 { /eq } .
Step 2 : nowadays looking at the { equivalent } y { /eq } -axis, we see that the largest interval of { equivalent } y { /eq } -values for which there is a graph to the left field of, the right of, or on the { equivalent } y { /eq } -axis is the interval from y = -4 to y = 8, not including 8. Again, 8 is not included because there is no decimal point on the graph whose { equivalent } y { /eq } -coordinate is 8. consequently, the range of { equivalent } f { /eq } is the interval { equivalent } [ -4,8 ) { /eq }. Equivalently, the range is { equivalent } -4 \le y < 8 { /eq } .
Finding Domain & Range from the Graph of a Continuous Function: Example 2
Use the graph of { equivalent } gigabyte { /eq } below to determine the knowledge domain and stove of { equivalent } guanine { /eq } .
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Step 1 : The time interval of { equivalent } x { /eq } -values that make up the laid of all { equivalent } x { /eq } -coordinates of points on the graph is { equivalent } [ -3, \infty ) { /eq }, because the graph starts at { equivalent } ( -3,0 ) { /eq } and continues on forever to the right. That is, the domain of { equivalent } gram { /eq } is { equivalent } [ -3, \infty ) { /eq }. Equivalently, the knowledge domain is { equivalent } x\ge -3 { /eq }.
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Step 2 : The interval of { equivalent } y { /eq } -values that make up the bent of all { equivalent } y { /eq } -coordinates of points on the graph is { equivalent } [ 0, \infty ) { /eq }, because the graph starts at { equivalent } ( -3,0 ) { /eq } and continues up forever. That is, the range of { equivalent } g { /eq } is { equivalent } [ 0, \infty ) { /eq }. Equivalently, the image is { equivalent } y\ge 0 { /eq } .
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