algebra 2a - unit 4: more about polynomial functions

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)