algebra 2a - unit 4: exam

the rule of a function changes from f(x) = (3x)^3 − 8 to g(x) = (9x)^3 − 8 when it is dilated. which statement best describes how this dilation affects the graph of f(x)?

XXX the graph is stretched away from the x-axis by a factor of 1/3

if the rule of the function for f(x) is f(x) = x^2 − 4, what is the rule of the function for g(x)?

g(x) = (x - 5)^2 - 4

which graph represents the function that has the rule f(x) = (x + 4)^2(x − 2)^2?

https://assets.learnosity.com/organisations/625/asset/media/1237143

the rule of a function changes from f(x) = 6(x − 3)^2 + 12 to g(x) = 2(x − 3)^2 + 4 when it is dilated. which statement best describes how this dilation affects the graph of f(x)?

the graph is compressed toward the x-axis by a factor of 1/3

the rule of a function changes from f(x) = 12x^4 + 4 to g(x) = 3x^4 + 1 when it is dilated. which statement best describes how this dilation affects the graph of f(x)?

the graph is compressed toward the x-axis by a factor of 1/4

the rule of a function changes from f(x) = −2(x − 1)^4 + 7 to g(x) =(x − 1)^4 − 72 when two transformations are performed. which statement best describes how these transformations affect the graph of f(x)?

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

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

the graph moved left 3 units

if the rule of the function is f(x) = (x − 2)^3 + 3, what is the rule of the function for g(x)?

g(x) = 2(-x - 2)^3 + 6

the rule of a function changes from f(x) = (6x)^4 + 4 to g(x) = (12x)^4 + 4 when it is dilated. which statement best describes how this dilation affects the graph of f(x)?

XXX the graph is stretched away from the x-axis by a factor of 1/2

consider the graph of f(x) FROM QUESTION 1. which statements are true about the function represented by the graph? select all that apply.

the function has two relative minima, both 0, and one relative maximum of 25.6. as approaches negative infinity, f(x) approaches infinity, and as x approaches infinity, f(x) approaches infinity. the function increases over the intervals (−3, −0.7) and (1.5, ∞), and it decreases over the intervals (−∞, −3) and (−0.7, 1.5)

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

the function is positive over the intervals (−∞, −4), (−4, 2), and (2, ∞). as x approaches −∞, f(x) approaches ∞, and as x approaches ∞, f(x) approaches ∞. the function has relative minima at (−4, 0) and (2, 0), and it has a relative maximum between the x-values −4 and 2.

the rule of a function changed from f(x) = x^4 + 2x^3 − 11 to g(x) = x^4 + 2x^3 + 4 when it was translated. which statement best describes how this translation affected the graph of f(x)?

the graph slid up 15 units

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

the y-intercept is (0, 64) the x-intercept are (-4, 0) and (2, 0) the zeros of the function are x = -4 and x = 2

consider the graph of f(x). https://assets.learnosity.com/organisations/625/asset/media/1237121 which statements are true about the function represented by the graph? select all that apply.

the zeros of the function are x = -3 and x = 1.5 the x-intercepts are (-3, 0), (1.5, 0), and the y-intercept is (0, 20.3) the domain of the function is (−∞, ∞), and the range of the function is [0, ∞)

which graph best represents the translation of function f(x) = x^3 + 5x^2 to function g(x) = x^3 + 5x^2 - 4?

https://assets.learnosity.com/organisations/625/asset/media/1237216

which graph best represents the translation of function f(x) = x(x − 2)^2 − 2 to function g(x) = 3x(x − 2)^2 − 6?

https://assets.learnosity.com/organisations/625/asset/media/1237236

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

https://assets.learnosity.com/organisations/625/asset/media/1237240

which graph best represents the translation of function f(x) = −x^2(x − 1)(x + 2) + 5 to function g(x) = (2x)^2(2x − 1)(2x + 2) − 5?

https://assets.learnosity.com/organisations/625/asset/media/1237244