Nonlinear Functions - Sample Math Practice Problems

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Complexity=5, Mode=quadratic

Give the equation of this quadratic function. It should be in the form of 'y = nx²' where n is an integer. Type x² as x^2, etc.

1.

2.

Complexity=3, Mode=cubic

Give the equation of this cubic function. It should be in the form of 'y = nx³' where n is an integer. Type x² as x^2, etc.

1.

2.

Complexity=5, Mode=mixed

Give the equation of the following functions. They may be quadratic or cubic functions. They should be of the form 'y = nx² + b' or 'y = nx³ + b' where n and b are integers. Type x² as x^2, etc.

1.

2.

Answers

Complexity=5, Mode=quadratic

Give the equation of this quadratic function. It should be in the form of 'y = nx²' where n is an integer. Type x² as x^2, etc.

#	Problem	Correct Answer	Your Answer
1
Solution The parabola opens upward so we know that, in y = nx2, n > 0. We also know (2, 8) is on the parabola. So 8 = n * 22 8 = 4n n = 2 So y = 2x2

#	Problem	Correct Answer	Your Answer
2
Solution The parabola opens downward so we know that, in y = nx2, n < 0. We also know (2, -8) is on the parabola. So -8 = n * 22 -8 = 4n n = -2 So y = -2x2

Complexity=3, Mode=cubic

Give the equation of this cubic function. It should be in the form of 'y = nx³' where n is an integer. Type x² as x^2, etc.

#	Problem	Correct Answer	Your Answer
1
Solution The cubic function increases as x increases so we know n > 0. (2, 8) is in the cubic function. y = nx3 8 = n * 23 8 = 8n n = 1 y = x3

#	Problem	Correct Answer	Your Answer
2
Solution The cubic function decreases as x increases so we know n < 0. (2, -16) is in the cubic function. y = nx3 -16 = n * 23 -16 = 8n n = -2 y = -2x3

Complexity=5, Mode=mixed

Give the equation of the following functions. They may be quadratic or cubic functions. They should be of the form 'y = nx² + b' or 'y = nx³ + b' where n and b are integers. Type x² as x^2, etc.

#	Problem	Correct Answer	Your Answer
1
Solution The function decreases as x increases and doesn't open in a direction like a parabola, so it is a cubic function of the form y = nx3 + b with n < 0. The equation intersects the y-axis at(0, -1), so y = nx3 + b -1 = n * 03 + b -1 = b y = nx3 -1 We also know (1, -3) is in the parabola. -3 = n * 13 -1 -3 = n -1 n = -2 y = -2x3 -1

#	Problem	Correct Answer	Your Answer
2
Solution The function decreases as x increases and doesn't open in a direction like a parabola, so it is a cubic function of the form y = nx3 + b with n < 0. The equation intersects the y-axis at(0, 3), so y = nx3 + b 3 = n * 03 + b 3 = b y = nx3 + 3 We also know (1, 2) is in the parabola. 2 = n * 13 + 3 2 = n + 3 n = -1 y = -x3 + 3