Describe the end behavior of the graph of the function.

h(x) → - ∞ as x → - ∞ and h(x) → - ∞ as x → ∞

h(x) → ∞ as x → - ∞ and h(x) → - ∞ as x → ∞

h(x) → - ∞ as x → - ∞ and h(x) → ∞ as x → ∞

h(x) → ∞ as x → - ∞ and h(x) → ∞ as x → ∞

Describe the transformation of f(x) represented by g(x). Check by graphing each function.

The graph of g(x) is a translation 4 units right and 5 units down of the graph of f(x).

The graph of g(x) is a translation 5 units right and 4 units down of the graph of f(x).

The graph of g(x) is a translation 4 units left and 5 units down of the graph of f(x).

The graph of g(x) is a translation 4 units left and 5 units up of the graph of f(x).

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

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)→-∞

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

Translation 1 unit right and 4 units up.

Translation 1 unit left and 4 units up.

Translation 4 units right and 1 unit down.

Translation 4 units left and 1 unit down.

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

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

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.

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

Increasing (-∞, -2.26); decreasing (-2.26, -0.07); increasing (-0.07, ∞)

Increasing (-∞, -2.26) & decreasing (-2.26, ∞)

Decreasing (-∞, -0.07) & increasing (-0.07, ∞)

Decreasing (-∞, -2.26); increasing (-2.26, -0.07); decreasing (-0.07, ∞)

If the yellow curve has equation f(x) = x 2 , and the blue curve, g(x) , is the transformation of f(x) , then...

Then the blue curve is g(x) = f(x + c)

Then the blue curve is g(x) = f(x) - c

Then the blue curve is g(x) = f ( x - c)

Then the blue curve is g(x) = f(x ) + c

Polynomial Transformation

Authored by Ramon Rasaq

Mathematics

9th Grade - University

CCSS covered

Used 21+ times

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25 questions

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MULTIPLE CHOICE QUESTION

2 mins • 1 pt

What is the equation for the red function?

g(x)=x³+1

g(x)=x³-1

g(x)=(x-1)³

g(x)=(x+1)³

Tags

CCSS.HSA.APR.A.1

CCSS.HSA.REI.D.11

MULTIPLE CHOICE QUESTION

3 mins • 1 pt

If f(x) = x³ is changed to f(x) = - (x + 3)³ + 2, how is the graph transformed?

3 units right, 2 units up, reflected across the y-axis

3 units right, 2 units up, reflected across the x-axis

3 units left, 2 units up, reflected across the y-axis

3 units left, 2 units up, reflected across the x-axis

Tags

CCSS.HSF.BF.B.3

MULTIPLE CHOICE QUESTION

2 mins • 1 pt

List the transformations to the parent function in y = -(x + 4)²- 3

reflect over y, right 4, down 3

reflect over y, left 4 down 3

reflect over x, right 4, down 3

reflect over x, left 4, down 3

Tags

CCSS.HSF.BF.B.3

CCSS.HSG.CO.A.2

MULTIPLE CHOICE QUESTION

3 mins • 1 pt

Which could be the resulting function?

g(x)= 1.5 (x - 3) + 4

g(x)= 0.6 (x + 3) + 4

g(x)= 2 (x - 3) + 4

g(x)= 2 (x + 3) + 4

Tags

CCSS.HSF.BF.B.3

MULTIPLE CHOICE QUESTION

1 min • 1 pt

If g(x) is a transformation of f(x) and g(x) = af(x + b) + c, what effect does c have on the transformation?

Shift up c units

Shift down c units

Shift right c units

Shift left c units

Tags

CCSS.HSF.BF.B.3

CCSS.HSG.CO.A.2

MULTIPLE CHOICE QUESTION

1 min • 1 pt

If g(x) is a transformation of f(x) and g(x) = af(x + b) + c, what effect does b have on the transformation?

Shift up b units

Shift down b units

Shift right b units

Shift left b units

Tags

CCSS.HSF.BF.B.3

CCSS.HSG.CO.A.2

MULTIPLE CHOICE QUESTION

1 min • 1 pt

If g(x) is a transformation of f(x) and g(x) = af(x + b) + c, what effect does a have on the transformation?

Shift up a units

Make the graph wider or narrower

Shift right a units

Reflect the graph over the x-axis

Tags

CCSS.HSF.BF.B.3

CCSS.HSG.CO.A.2

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Polynomial Transformation

What is the equation for the red function?

If f(x) = x³ is changed to f(x) = - (x + 3)³ + 2, how is the graph transformed?

List the transformations to the parent function in y = -(x + 4)²- 3

Which could be the resulting function?

If g(x) is a transformation of f(x) and g(x) = af(x + b) + c, what effect does c have on the transformation?

If g(x) is a transformation of f(x) and g(x) = af(x + b) + c, what effect does b have on the transformation?

If g(x) is a transformation of f(x) and g(x) = af(x + b) + c, what effect does a have on the transformation?

The graph shows the function f(x)=x² in blue and another function g(x) in red. Which could be the equation for g(x)?

Describe the end behavior of the graph of the function.

This is the graph of which polynomial function?

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Similar Resources on Wayground

Popular Resources on Wayground

Discover more resources for Mathematics

Polynomial Transformation

What is the equation for the red function?

If f(x) = x3 is changed to f(x) = - (x + 3)3 + 2, how is the graph transformed?

List the transformations to the parent function in y = -(x + 4)2- 3

Which could be the resulting function?

If g(x) is a transformation of f(x) and g(x) = af(x + b) + c, what effect does c have on the transformation?

If g(x) is a transformation of f(x) and g(x) = af(x + b) + c, what effect does b have on the transformation?

If g(x) is a transformation of f(x) and g(x) = af(x + b) + c, what effect does a have on the transformation?

The graph shows the function f(x)=x2 in blue and another function g(x) in red. Which could be the equation for g(x)?

Describe the end behavior of the graph of the function.

This is the graph of which polynomial function?

Access all questions and much more by creating a free account

Similar Resources on Wayground

Popular Resources on Wayground

Discover more resources for Mathematics

If f(x) = x³ is changed to f(x) = - (x + 3)³ + 2, how is the graph transformed?

List the transformations to the parent function in y = -(x + 4)²- 3

The graph shows the function f(x)=x² in blue and another function g(x) in red. Which could be the equation for g(x)?