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Which of the following is an example of a function whose graph in the xy-plane has no x-intercepts?
- a)A linear function whose rate of change is not zero
- b)A quadratic function with real zeros
- c)A quadratic function with no real zeros
- d)A cubic polynomial with at least one real zero
Correct answer is option 'C'. Can you explain this answer?
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Which of the following is an example of a function whose graph in the ...
Quadratic Function with no Real Zeros
Quadratic functions are represented by equations of the form y = ax^2 + bx + c. The x-intercepts of a function are the points where the graph intersects the x-axis, meaning the y-coordinate is zero. In the case of a quadratic function, the x-intercepts are the roots of the equation, which can be found using the quadratic formula: x = (-b ± √(b^2 - 4ac)) / 2a.
- Real Zeros: A quadratic function with real zeros has x-intercepts where the graph crosses the x-axis at real number values of x.
- No Real Zeros: If the discriminant (b^2 - 4ac) in the quadratic formula is negative, the function will have no real zeros. This means the graph of the function will not intersect the x-axis at any real number values of x.
In this case, the function will not have any x-intercepts, as the graph will either lie entirely above or below the x-axis. Therefore, a quadratic function with no real zeros is an example of a function whose graph in the xy-plane has no x-intercepts.
Quadratic functions are represented by equations of the form y = ax^2 + bx + c. The x-intercepts of a function are the points where the graph intersects the x-axis, meaning the y-coordinate is zero. In the case of a quadratic function, the x-intercepts are the roots of the equation, which can be found using the quadratic formula: x = (-b ± √(b^2 - 4ac)) / 2a.
- Real Zeros: A quadratic function with real zeros has x-intercepts where the graph crosses the x-axis at real number values of x.
- No Real Zeros: If the discriminant (b^2 - 4ac) in the quadratic formula is negative, the function will have no real zeros. This means the graph of the function will not intersect the x-axis at any real number values of x.
In this case, the function will not have any x-intercepts, as the graph will either lie entirely above or below the x-axis. Therefore, a quadratic function with no real zeros is an example of a function whose graph in the xy-plane has no x-intercepts.
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Which of the following is an example of a function whose graph in the ...
If f is a function of x, then the graph of f in the xy-plane consists of all points (x, f(x)). An x-intercept is where the graph intersects the x-axis; since all points on the x-axis have y-coordinate 0, the graph of f will cross the x-axis at values of x such that f(x) = 0. Therefore, the graph of a function f will have no x-intercepts if and only if f has no real zeros. Likewise, the graph of a quadratic function with no real zeros will have no x-intercepts.
Choice A is incorrect. The graph of a linear function in the xy-plane whose rate of change is not zero is a line with a nonzero slope. The x-axis is a horizontal line and thus has slope 0, so the graph of the linear function whose rate of change is not zero is a line that is not parallel to the x-axis. Thus, the graph must intersect the x-axis at some point, and this point is an x-intercept of the graph. Choices B and D are incorrect because the graph of any function with a real zero must have an x-intercept.
Choice A is incorrect. The graph of a linear function in the xy-plane whose rate of change is not zero is a line with a nonzero slope. The x-axis is a horizontal line and thus has slope 0, so the graph of the linear function whose rate of change is not zero is a line that is not parallel to the x-axis. Thus, the graph must intersect the x-axis at some point, and this point is an x-intercept of the graph. Choices B and D are incorrect because the graph of any function with a real zero must have an x-intercept.
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Which of the following is an example of a function whose graph in the xy-plane has no x-intercepts?a)A linear function whose rate of change is not zerob)A quadratic function with real zerosc)A quadratic function with no real zerosd)A cubic polynomial with at least one real zeroCorrect answer is option 'C'. Can you explain this answer?
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Which of the following is an example of a function whose graph in the xy-plane has no x-intercepts?a)A linear function whose rate of change is not zerob)A quadratic function with real zerosc)A quadratic function with no real zerosd)A cubic polynomial with at least one real zeroCorrect answer is option 'C'. Can you explain this answer? for SAT 2025 is part of SAT preparation. The Question and answers have been prepared according to the SAT exam syllabus. Information about Which of the following is an example of a function whose graph in the xy-plane has no x-intercepts?a)A linear function whose rate of change is not zerob)A quadratic function with real zerosc)A quadratic function with no real zerosd)A cubic polynomial with at least one real zeroCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for SAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Which of the following is an example of a function whose graph in the xy-plane has no x-intercepts?a)A linear function whose rate of change is not zerob)A quadratic function with real zerosc)A quadratic function with no real zerosd)A cubic polynomial with at least one real zeroCorrect answer is option 'C'. Can you explain this answer?.
Which of the following is an example of a function whose graph in the xy-plane has no x-intercepts?a)A linear function whose rate of change is not zerob)A quadratic function with real zerosc)A quadratic function with no real zerosd)A cubic polynomial with at least one real zeroCorrect answer is option 'C'. Can you explain this answer? for SAT 2025 is part of SAT preparation. The Question and answers have been prepared according to the SAT exam syllabus. Information about Which of the following is an example of a function whose graph in the xy-plane has no x-intercepts?a)A linear function whose rate of change is not zerob)A quadratic function with real zerosc)A quadratic function with no real zerosd)A cubic polynomial with at least one real zeroCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for SAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Which of the following is an example of a function whose graph in the xy-plane has no x-intercepts?a)A linear function whose rate of change is not zerob)A quadratic function with real zerosc)A quadratic function with no real zerosd)A cubic polynomial with at least one real zeroCorrect answer is option 'C'. Can you explain this answer?.
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