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What is the range of the graph of a linear function?

A. y = -1
B. y < -1
C. x > -1
D. x > 1
Other: ________

User Smnbss
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1 Answer

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Final answer:

The range of the graph of a linear function with a non-zero slope is all real numbers, as the function extends infinitely in the y-direction. However, if the slope is zero, the range is a single value, exactly equal to the y-intercept.

Step-by-step explanation:

The range of the graph of a linear function is all possible y-values that the function can take. Since a linear function is defined by an equation of the form y = a + bx, where a is the y-intercept and b is the slope, the range depends on the value of the slope b. If b is not zero, the graph of a linear function is a line with either a positive or negative slope, which extends infinitely in the y-direction meaning that the range is all real numbers. However, if b equals zero, the graph is horizontal and therefore has a range that consists of a single value, exactly equal to the y-intercept a.

For example, looking at Practice Test 4:

  • Equation A (y = -3x) is a linear function with a negative slope, implying that as x increases y decreases, and the range is all real numbers.
  • Equation B (y = 0.2 +0.74x) is a linear function with a positive slope, suggesting that as x increases y also increases, and likewise, the range is all real numbers.
  • Equation C (y=-9.4 - 2x), similar to Equation A, is a linear function that slopes downward to the right, and the range again is all real numbers.


Therefore, the correct answer to the original question would be

Other: All real numbers

, since both increasing and decreasing lines extend infinitely in the y-direction.

User Peter Kriens
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