Cubic Functions and Square Root Functions

What are the key features of a cubic function?

• The key features of a cubic function are that it is a trigonometric function and its graph is a circle

• The key features of a cubic function are that it is a linear function and its graph is a parabola

• The key features of a cubic function are that it is a polynomial function of degree 3 and its graph is a curve with one or more inflection points.

• The key features of a cubic function are that it is a polynomial function of degree 2 and its graph is a straight line

Explain the relationship between the roots and the x-intercepts of a cubic function.

• The roots of a cubic function are the reciprocals of the x-intercepts.

• The roots of a cubic function are the square roots of the x-intercepts.

• The roots of a cubic function are the same as the x-intercepts.

• The roots of a cubic function are unrelated to the x-intercepts.

Find the domain and range of the square root function f(x) = √(x-3).

• The domain is x = 3 and the range is y = 0.

• The domain is x > 3 and the range is y > 0.

• The domain is x ≤ 3 and the range is y ≤ 0.

• The domain is x ≥ 3 and the range is y ≥ 0.

• x = -1, x = 1, x = 2

• x = -2, x = 2, x = 4

• x = -6, x = 0, x = 6

• x = -3, x = 5, x = 16

Tags

CCSS.HSF-IF.C.7C

Determine the domain and range of the square root function g(x) = √(2x + 5).

• Domain: x < -2.5, Range: y < 0

• Domain: x ≥ -2.5, Range: y ≥ 0

• Domain: x ≤ -2.5, Range: y ≤ 0

• Domain: x > 2.5, Range: y > 0

What is the relationship between the turning points and the roots of a cubic function?

• The turning points are always the same as the roots of a cubic function.

• The turning points are located at the same x-values as the roots of a cubic function.

• The turning points are always greater than the roots of a cubic function.

• The turning points are not necessarily the same as the roots of a cubic function.

What is the relationship between the turning points and the roots of a quadratic function?

• The turning points are always the same as the roots of a quadratic function.

• The turning points are located at the same x-values as the roots of a quadratic function.

• The turning points are always greater than the roots of a quadratic function.

• The turning points are not necessarily the same as the roots of a quadratic function.

Tags

CCSS.HSF-IF.C.7A

• -2.828, -2, 2.828

• -2, 2, 4

• 0, -2, 2

• -10 , -3.21, 3.21

Tags

CCSS.HSF-IF.C.7C

Explain how to identify the end behavior of a cubic function.

• Examine the vertex of the function

• Count the number of x-intercepts

• Look at the constant term in the function

• Look at the leading coefficient and the degree of the function.

• Domain: x ≥ 3, Range: y ≥ 0

• Domain: x ≤ 3, Range: y ≤ 0

• Domain: x > 3, Range: y > 0

• Domain: x ≤ 3, Range: y > 0