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The graph of the function f in the xy-plane crosses the x-axis at -4, 2, and 5. Which of the following could define f?
- a)f(x) = (x - 2)2(x - 5)
- b)f(x) = (x2 + 2x - 8)(3x -15)
- c)f(x) = (x2 - 7x + 10)(x - 4)
- d)f(x) = (x - 4)(x + 2)(x + 5)
Correct answer is option 'B'. Can you explain this answer?
Verified Answer
The graph of the function f in the xy-plane crosses the x-axis at -4, ...
The points where the graph of a function crosses the x axis correspond to those values of x for which the function equals zero. To solve this problem, factor each answer choice and apply the Zero Product Property to see which function equals zero at x = -4, x = 2, and x = 5:
A) 0 = (x - 2)2(x - 5), so x = 2 or x = 5 (nope)
B) 0 = (x2 + 2x - 8)(3x - 15) = (x + 4)(x - 2)(3x - 15),
so x = -4 or x = 2 or x = 5 (yes!)
C) 0 = (x2 - 7x + 10)(x - 4) = (x - 5)(x - 2)(x - 4),
so x = 5 or x = 2 or x = 4 (nope)
D) 0 = (x - 4)(x + 2)(x + 5),
so x = 4 or x = -2 or x = -5 (nope)
Alternatively, you can plug the three intercept values into each function and see which function equals zero for all three of them.
A) 0 = (x - 2)2(x - 5), so x = 2 or x = 5 (nope)
B) 0 = (x2 + 2x - 8)(3x - 15) = (x + 4)(x - 2)(3x - 15),
so x = -4 or x = 2 or x = 5 (yes!)
C) 0 = (x2 - 7x + 10)(x - 4) = (x - 5)(x - 2)(x - 4),
so x = 5 or x = 2 or x = 4 (nope)
D) 0 = (x - 4)(x + 2)(x + 5),
so x = 4 or x = -2 or x = -5 (nope)
Alternatively, you can plug the three intercept values into each function and see which function equals zero for all three of them.
Most Upvoted Answer
The graph of the function f in the xy-plane crosses the x-axis at -4, ...
Explanation:
Given Information: The graph of the function f crosses the x-axis at -4, 2, and 5.
Analysis: To find the equation that defines the function f, we need to consider the roots of the function. The roots are the x-values where the graph crosses the x-axis.
Roots of f: -4, 2, and 5
Function f(x) = (x2 + 2x - 8)(3x - 15):
- This function has roots at x = -4, x = 2, and x = 5.
- The roots are obtained by setting each factor to zero.
- (x2 + 2x - 8) = 0 gives x = -4 or x = 2
- (3x - 15) = 0 gives x = 5
Conclusion: Option B, f(x) = (x2 + 2x - 8)(3x - 15), is the correct choice because it has roots at -4, 2, and 5 as given in the question.
Given Information: The graph of the function f crosses the x-axis at -4, 2, and 5.
Analysis: To find the equation that defines the function f, we need to consider the roots of the function. The roots are the x-values where the graph crosses the x-axis.
Roots of f: -4, 2, and 5
Function f(x) = (x2 + 2x - 8)(3x - 15):
- This function has roots at x = -4, x = 2, and x = 5.
- The roots are obtained by setting each factor to zero.
- (x2 + 2x - 8) = 0 gives x = -4 or x = 2
- (3x - 15) = 0 gives x = 5
Conclusion: Option B, f(x) = (x2 + 2x - 8)(3x - 15), is the correct choice because it has roots at -4, 2, and 5 as given in the question.
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The graph of the function f in the xy-plane crosses the x-axis at -4, 2, and 5. Which of the following could define f?a)f(x) = (x - 2)2(x - 5)b)f(x) = (x2 + 2x - 8)(3x -15)c)f(x) = (x2 - 7x + 10)(x - 4)d)f(x) = (x - 4)(x + 2)(x + 5)Correct answer is option 'B'. Can you explain this answer?
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