5.1,7&8 Graphing Polynomials

State the degree, type, and leading coefficient for this polynomial.

• Degree is 4, quartic, leading coefficient is 2
• Degree is 3, cubic, leading coefficient is √14
• Degree is 2, quadratic, leading coefficient is ⅓
• Degree is 2, cubic, leading coefficient is 4

Tags

CCSS.HSA.APR.A.1

Describe the end behavior of the graph of the function.

• As x→+∞ , h(x)→+∞ ; and as x→-∞ , h(x)→-∞
• As x→+∞ , h(x)→-∞ ; and as x→-∞ , h(x)→+∞
• As x→+∞ , h(x)→+∞ ; and as x→-∞ , h(x)→+∞
• As x→+∞ , h(x)→-∞ ; and as x→-∞ , h(x)→-∞

Tags

CCSS.HSA.APR.A.1

CCSS.HSF.IF.B.4

CCSS.HSF.IF.C.7

Describe the transformation of f(x) represented by g(x).

• Translation 1 unit left and 4 units up.
• Translation 4 units right and 1 unit down.
• Translation 1 unit right and 4 units up.
• Translation 4 units left and 1 unit down.

Tags

CCSS.HSF.BF.B.3

Describe the graph of g(x) as a transformation of the graph of f(x).

• Reflection in the y-axis, followed by a vertical stretch by a factor of 4.
• Reflection in the x-axis, followed by a vertical stretch by a factor of 4.
• Reflection in the y-axis, followed by a vertical shrink by a factor of ¼.
• Reflection in the x-axis, followed by a vertical shrink by a factor of ¼.

Tags

CCSS.HSF.BF.B.3

CCSS.HSF.IF.C.7

• f(x) = ⅕ (x+3) (x+4) (x-8)
• g(x) = ½ (x-4) (x+3) (x-6)
• h(x) = ⅕ (x-3) (x-4) (x+8)
• p(x) = ½ (x+4) (x-3) (x+6)

Tags

CCSS.HSA.APR.A.1

CCSS.HSA.APR.B.3

CCSS.HSA.REI.D.10

CCSS.HSA.REI.D.11

Find all real zeros of the function.

• -⁵/₂ , -2 , 1
• 1 , 2 , 3
• 2 , 7 , 1
• -1 , 2 , ⁵/₂

Identify the points where the local maximum(s) and local minimum(s) occur.

• (-2.26, 0.407) is a local minimum; (-0.0738, -10.036) is a local maximum
• (-2.26, 0.407) is a local maximum; (-0.0738, -10.036) is a local minimum
• (1, 0) is a local maximum; (0, -10) is a local minimum
• no local maximum; (0, -10) is an absolute minimum

Determine the intervals for which the function is increasing and decreasing.

• Increasing (-∞, -2.26) & decreasing (-2.26, ∞)
• Decreasing (-∞, -0.07) & increasing (-0.07, ∞)
• Decreasing (-∞, -2.26); increasing (-2.26, -0.07); decreasing (-0.07, ∞)
• Increasing (-∞, -2.26); decreasing (-2.26, -0.07); increasing (-0.07, ∞)

Tags

CCSS.HSA.APR.B.3

CCSS.HSF.IF.B.4

CCSS.HSF.IF.C.7

Identify the possible degree of the function.

• 1
• 2
• 3
• 4

Evaluate the function for the given value of x. 

• ²⁷/₈
• - ⅝
• - ²⁷/₈
• ⅝