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.