algebra 2a - unit 4: more about polynomial functions

Pataasin ang iyong marka sa homework at exams ngayon gamit ang Quizwiz!

examine the graph, where the function f(x) is the preimage, and the function g(x) is an image of a dilation. https://cdstools.flipswitch.com/asset/media/1237235 if the rule of one function is f(x) = (2x − 4)^3 + 5, what is the rule of the function for g(x)?

(x - 4)^3 + 5

https://cdstools.flipswitch.com/asset/media/1237120 which function rule does the graph represent?

(x − 1)(x + 2)(x − 4)(x − 2.5)

examine the graph, where the function f(x) is the preimage and the function g(x) is an image of a translation. https://cdstools.flipswitch.com/asset/media/1237202 if g(x) = f(x) + k, what is the value of k?

-11

examine the graph, where the function f(x) is the preimage, and the function g(x) is an image of a dilation. https://cdstools.flipswitch.com/asset/media/1237233 if g(x) = af(x), what is the value of a?

2

examine the graph, where the function f(x) is the preimage, and the function g(x) is an image of a translation. https://cdstools.flipswitch.com/asset/media/1237215 if g(x) = f(x - h), what is the value of h?

3

consider the graph of f(x). https://cdstools.flipswitch.com/asset/media/1237117 which statements are true about the function represented by the graph? select all that apply.

XXX the function has two relative minima, which are −2.1 and 1.6, and a relative maximum, which is 0.5 as x approaches negative infinity, f(x) approaches negative infinity, and as x approaches infinity, f(x) approaches negative infinity. the function increases over the intervals (−∞, −2.1) and (0.5, 1.6), and it decreases over the intervals (−2.1, 0.5) and (1.6,∞).

consider the graph of f(x). https://cdstools.flipswitch.com/asset/media/1237118 which statements are true about the function represented by the graph? select all that apply.

XXXX the function has two relative maxima, both 0, and a relative minimum of −9.4 as x approaches negative infinity, f(x) approaches negative infinity, and as x approaches infinity, f(x) approaches infinity. the function increases over the intervals (−1, 0.7) and (2.5, ∞), and it decreases over the intervals (−∞, −1) and (0.7, 2.5)

which statements are true about the function f(x) = -(x + 3)^4? select all that apply.

as x approaches -∞, f(x) approaches -∞, and as x approaches ∞, f(x) approaches -∞. the function has a relative maximum at x = -3 the function is negative over the intervals (-∞, -3) and (-3, ∞)

part 2: which statements are true about the function f(x) = -2x^4 - 2x^3 + 18x^2 + 18x? select all that apply.

as x approaches -∞, f(x) approaches -∞, and as x approaches ∞, f(x) approaches -∞. the function has relative maxima over the intervals (-3, -1) and (0, 3), and it has a relative minimum over the interval (-1, 0) the function is positive over the intervals (-3, -1) and (0, 3), and it is negative over the intervals (-∞, -3), (-1, 0), and (3, ∞)

which statements are true about the function f(x) = (x - 2)^2(x - 0.5)(x + 2.5)? select all that apply.

as x approaches -∞, f(x) approaches ∞, and as x approaches ∞, f(x) approaches ∞. the function has a relative maximum over the interval (0.5, 2), and it has relative minima over the interval (-2.5, 0.5) and at point (2, 0) the function is positive over the intervals (-∞, -2.5), (0.5, 2), and (2, ∞), and it is negative over the interval (-2.5, 0.5)

which statements are true about the function f(x) = 5x^4 + 15x^3 - 20x^2 - 60x? select all that apply.

as x approaches -∞, f(x) approaches ∞, and as x approaches ∞, f(x) approaches ∞. the function has relative minima between the x-values -3 and -2 and between the x-values 0 and 2 and it has a relative maximum between the x-values -2 and 0 the function is positive over the intervals (-∞, -3), (-2, 0), and (2, ∞), and it is negative over the intervals (-3, -2) and (0, 2)

which statements are true about the function f(x) = x(x - 2)(x + 6)(x + 1)? select all that apply.

as x approaches -∞, f(x) approaches ∞, and as x approaches ∞, f(x) approaches ∞. the function is positive over the intervals (-∞, -6), (-1, 0), and (2, ∞), and it is negative over the intervals (-6, -1) and (0, 2). the function has relative minima between the x-values -6 and -1 and between the x-values 0 and 2, and it has a relative maximum between the x-values -1 and 0.

lesson 18

dilations of polynomial functions

if g(x) = f(x) - 1, then g(x) slides the function f(x) 1 unit ____. which word correctly fills in the blank in the previous sentence?

downward

examine the graph, where the function f(x) is the preimage and the function g(x) is an image of a translation. https://cdstools.flipswitch.com/asset/media/1237203 if the rule of the function for f(x) is f(x) = −(x + 6)^4, what is the rule of the function for g(x)?

g(x) = -(x - 1)^4

examine the graph, where the function f(x) is the preimage, and the function g(x) is an image of a dilation. https://cdstools.flipswitch.com/asset/media/1237234 if the rule of one function is f(x) = −(x + 2)^4 + 6, what is the rule of the function for g(x)?

g(x) = -2(x + 2)^4 + 12

examine the graph, which contains two parabolas. f(x) is a parabola that opens upward with its vertex at (−5, −9). it is the graph of the quadratic function f(x) = (x + 5)^2 − 9, and it represents the preimage for a transformation. g(x) is a parabola that opens upward with its vertex at (7, −3). tt represents the image of the transformation. which function rule for g(x) correctly describes the transformation in the graph?

g(x) = f(x - 12) + 6

examine the graph, where the quartic function f(x) is the preimage, and the quartic function g(x) is an image of a translation. https://cdstools.flipswitch.com/asset/media/1237214 if the rule of the function for f(x) is f(x) = (x − 1)^2(x − 2)(x + 1), what is the rule of the function for g(x)?

g(x) = x(x − 2)^2(x − 3) − 3

which graph most accurately represents the translation of function f(x) = x^2 + 4x − 12 to function g(x) = x^2 + 4x − 4?

https://cdstools.flipswitch.com/asset/media/1237194

which graph best represents the translation of function f(x) = −x^3 + 5 to function g(x) = −(x + 2)^3 + 5?

https://cdstools.flipswitch.com/asset/media/1237198

which graph best represents the translation of function f(x) = x(x − 1)(x + 3) to function f′(x) = x(x − 1)(x + 3) − 7?

https://cdstools.flipswitch.com/asset/media/1237206

which graph best represents the translation of function f(x) = x^2 − 9 to function f′(x) = (x + 5)^2 − 6?

https://cdstools.flipswitch.com/asset/media/1237210

which graph best represents the dilation of function f(x) = x(x − 2)(x − 1) − 2 to function g(x) = 2x(x − 2)(x − 1) − 4?

https://cdstools.flipswitch.com/asset/media/1237225

which graph best represents the translation of function f(x) = −(x + 1)^3 + 5 to function g(x) = −(−x + 1)^3 + 5?

https://cdstools.flipswitch.com/asset/media/1237229

examine the graph, where the function p(x) is the preimage and the function i(x) is an image of a translation. https://cdstools.flipswitch.com/asset/media/1237204 which function rule for i(x) describes the correct transformation of p(x)?

i(x) = p(x) + 7

lesson 15

key features from graphs: quartic functions

lesson 16

key features from rules: quartic functions

consider the graph of f(x). https://cdstools.flipswitch.com/asset/media/1237095 which statements are true about the function represented by the graph? select all that apply.

the function has a maximum of 0. the function increases over the interval (−∞, 3), and it decreases over the interval (3, ∞) as x approaches negative infinity, f(x) approaches negative infinity, and as x approaches infinity, f(x) approaches negative infinity.

consider the graph of f(x). https://cdstools.flipswitch.com/asset/media/1237119 which statements are true about the function represented by the graph? select all that apply.

the function has one relative minimum of 0 the function increases over the interval (−1, ∞), and it decreases over the interval (−∞, −1) as x approaches negative infinity, f(x) approaches infinity, and as x approaches infinity, f(x) approaches infinity.

consider the graph of f(x) https://cdstools.flipswitch.com/asset/media/1237097 which statements are true about the function represented by the graph? select all that apply.

the function has one relative minimum, which is −7.9, and two relative maxima, which are 0 and 24.2 as x approaches negative infinity, f(x) approaches negative infinity, and as x approaches infinity, f(x) approaches negative infinity. the function increases over the intervals (−∞, 2) and (−0.5, 2.1), and it decreases over the intervals (−2, −0.5) and (2.1, ∞)

consider the graph of f(x). https://cdstools.flipswitch.com/asset/media/1237120 which statements are true about the function represented by the graph? select all that apply.

the function has two relative minima, which are −35 and −7, and one relative maximum, which is 4.8 as x approaches negative infinity, f(x) approaches infinity, and as x approaches infinity, f(x) approaches infinity. the function increases over the intervals (−1, 1.7) and (3.4, ∞), and it decreases over the intervals (−∞, −1) and (1.7, 3.4)

the rule of a function changes from f(x) = 6x^4 + 4 to g(x) = −3x^4 − 2 when two transformations are performed. which statement best describes how this dilation affects the graph of f(x)?

the graph is compressed by a factor of 1/2 and is reflected across the x-axis.

the rule of a function changes from f(x) = (6x)^4 + 4 to g(x) = (−12x)^4 + 4 when two transformations are performed. which statement best describes how this dilation affects the graph of f(x)?

the graph is compressed by a factor of 1/2 and is reflected across the y-axis.

the rule of a function changes from f(x) = x^2 − 4 to g(x) = −x^2 + 4 when it is dilated. which statement best describes how this dilation affects the graph of f(x)?

the graph is reflected across the x-axis.

the rule of a function changes from f(x) = (x - 2)^2 + 5 to g(x) = (-x - 2)^2 + 5 when it is dilated. which statement best describes how this dilation affects the graph of f(x)?

the graph is reflected across the y-axis.

the rule of a function changes from f(x) = (3x)^3 − 8 to g(x) = x^3 − 8 when it is dilated. which statement best describes how this dilation affects the graph of f(x)?

the graph is stretched by a factor of 3

the rule of a function changes from f(x) = x^3 − 8 to g(x) = 3x^3 − 24 when it is dilated. which statement best describes how this dilation affects the graph of f(x)?

the graph is stretched vertically by a factor of 3

the rule of a function changed from f(x) = x^2 − 6x + 8 to f′(x) = x^2 − 6x + 3 when it was translated. which statement best describes how this translation affected the graph?

the graph moved down 5 units.

the rule of a function changed from f(x) = x^4 − 2 to f′(x) = (x − 3)^4 + 2 when it was translated. which statement best describes how this translation affected the graph of f(x)?

the graph slid 3 units to the right and 4 units upward.

the rule of a function changed from f(x) = 2x^4 + x to g(x) = 2(x − 5)^4 + (x − 5) when it was translated. which statement best describes how this translation affected the graph of f(x)?

the graph slid 5 units to the right

the rule of a function changed from f(x) = x^3 − 2x + 8 to f′(x) = x^3 − 2x − 1 when it was translated. which statement best describes how this translation affected the graph of f(x)?

the graph slid 9 units downward

the rule of a function changed from f(x) = (x + 3)^4 to f′(x) = (x + 3)^4 + 11 when it was translated. which statement best describes how this translation affected the graph of f(x)?

the graph slid up 11 units

the rule of a function changed from f(x) = x(x + 1)(x − 3) − 1 to g(x) = (x + 2)(x + 3)(x − 1) + 1 when it was translated. which statement best describes how this translation affected the graph of f(x)?

the graphs slid 2 units up and 2 units to the left

part 2: which statements are true about the function f(x) = (x - 2)^2(x - 0.5)(x + 2.5)? select all that apply.

the y-intercept is (0, -5) the zeros are x = -2.5, x = 0.5, and x = 2 the x-intercepts are (-2.5, 0), (0.5, 0), and (2, 0)

which statements are true about the function f(x) = -(x + 3)^4? select all that apply.

the y-intercept is (0, -81) the zero of the function is x = -3 the function has one x-intercept, which is (-3, 0)

which statements are true about the function. f(x) = x(x - 2)(x + 6)(x + 1)?

the y-intercept is (0, 0) the x-intercept are (0, 0), (2, 0), (-6, 0), and (-1, 0) the zeros of the function are x = 0, x = -2, x = -6, and x = 1

which statements are true about the function f(x) = -2x^4 - 2x^3 + 18x^2 + 18x? select all that apply.

the y-intercept is (0, 0) the zeros are x = -3, x = -1, x = 0, x = 3 the x-intercepts are (-3, 0), (-1, 0), (0, 0), and (3, 0)

which statements are true about the function f(x) = 5x^4 + 15x^3 - 20x^2 - 60x? select all that apply.

the y-intercept is (0, 0) the zeros of the function are x = 0, x = 2, x = -2, and x = -3 the x-intercepts are (0, 0), (2, 0), (-2, 0), and (-3, 0)

consider the graph of f(x). https://cdstools.flipswitch.com/asset/media/1237119 which statements are true about the function represented by the graph? select all that apply.

the zero of the function is x = -1 the x-intercept is (-1, 0), and the y-intercept is (0, 1) the domain of the function is (−∞, ∞), and the range of the function is [0, ∞)

consider the graph of f(x). https://cdstools.flipswitch.com/asset/media/1237095 which statements are true about the function represented by the graph? select all that apply.

the zero of the function is x = 3 the x-intercept is (3, 0), and the y-intercept is (0, -81) the domain of the function is (−∞, ∞), and the range of the function is (−∞, 0).

consider the graph of f(x). https://cdstools.flipswitch.com/asset/media/1237118 which statements are true about the function represented by the graph? select all that apply.

the zeros of the function are x = -1 and x = 2.5 the x-intercepts are (-1, 0), (2.5, 0), and the y-intercept is (0, -6.3) the domain of the function is (−∞, ∞), and the range of the function is (−∞, 0]

consider the graph of f(x). https://cdstools.flipswitch.com/asset/media/1237097 which statements are true about the function represented by the graph? select all that apply.

the zeros of the function are x = -2, x = 0.5, and x = 3 the x-intercepts are (-2, 0), (0.5, 0), and (3,0), and the y-intercept is (0, -6) the domain of the function is (−∞, ∞), and the range of the function is (−∞, 24.2]

consider the graph of f(x). https://cdstools.flipswitch.com/asset/media/1237120 which statements are true about the function represented by the graph? select all that apply.

the zeros of the function are x = -2, x = 1, x = 2.5, and x = 4 the domain of the function is (−∞,∞), and the range of the function is [−35, ∞) the x-intercepts are(-2, 0), (1, 0), (2.5, 0), and (4, 0), and the y-intercept is (0, -20)

consider the graph of f(x). https://cdstools.flipswitch.com/asset/media/1237096 which statements are true about the function represented by the graph? select all that apply.

the zeros of the function are x = −3, x = 0, x = 1, and x = 2 the x-intercepts are (−3, 0), (0, 0), (1, 0), and (2, 0), and the y-intercept is (0, 0) the domain of the function is (−∞, ∞), and the range of the function is [−24.1, ∞)

if g(x) = f(x - 1), then g(x) translates the function f(x) 1 unit ____

to the right

lesson 17

translations of polynomial functions

if a polynomial of a function has the x-intercepts of 0, −2, 1, and 7, which expression can represent this function?

−x(x + 2)(x − 1)(x − 7)


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