algebra 2b - unit 5: more than one function

examine the table for f(x). which is the average rate of change for the function f(x) over the interval 0 ≤ x ≤ 5?

-0.45

consider the equations. f(x) = sin (2x) g(x) = -1/2x - 1 what are the values of x where f(x) = g(x)?

-0.45 -1.42 -2.91

consider the equations. f(x) = 4^x g(x) = -x^3 what is the closest estimate of x where f(x) = g(x)?

-0.72

what is the average rate of change for the function f(x) = x^3 - 6x^2 + 4x + 7 over the interval 0 <= x <= 5?

-1

consider the equations. f(x) = log_4 x g(x) = 2x^2 + 6x - 3 what are the values of x where f(x) = g(x)?

0.02, 0.33

consider the equations. f(x) = 2 cos(x) g(x) = (x + 0.5)^2 + 1 what are the values of x where f(x) = g(x)?

0.41, -0.93

consider the equations. f(x) = 2^x-4 g(x) = x^5 what is the closest estimate of x when f(x) = g(x)?

0.63

what is the average rate of change of f(x) over the interval -1 < x < 3?

1.364

checkpoint 21

100%

consider the equations. f(x) = log_3 x g(x) = -(x^2 - 8) what is the closest estimate of x where f(x) = g(x)?

2.67

consider the function f(x) = −√x and the graph of g(x). over which interval does f(x) decrease faster than g(x)?

[0, 1]

consider the function. f(x) = √3x+1 which interval has the greatest average rate of change in the given function?

[0, 3]

the table shows different values for functions f(x) and g(x), which are continuous for all x ≥ 0. over which intervals does f(x) = g(x)?

[2, 3] [3, 4]

the graph shows the function g(x). what is the average rate of change for each of the following intervals?

between 2 and 4 : increases by 1.415 per unit between 4 and 6 : increases by 0.585 per unit between 6 and 8 : increases by 0.45 per unit

examine the table for f(x) and the graph of g(x). both represent quadratic functions. which statement about the extrema of the functions is true?

the maximum of f(x) is 4 more than the maximum of g(x)

examine the table for f(x) and the graph for g(x). both represent quadratic functions. which statement about the vertices of the functions is true?

the maximum of f(x) is 5 less than the maximum of g(x)

compare the function f(x) = x^2 + 8x + 13 with the following graph of g(x). which statement is true?

the minimum of f(x) and the minimum of g(x) are equal.

compare the function f(x) = x^2 − 3x − 10 with the following graph of g(x). which statements about the intercepts are true? select all that apply.

the y-intercept of the rule f(x) is 7 units below the y-intercept of the graph g(x). both x-intercepts of the graph g(x) are between the x-intercepts of the rule f(x).

compare the function f(x) = x^2 + 3x − 4 with the following graph of g(x). which statements are true? select all that apply.

f(x) and g(x) both have an x-intercept at (-4, 0) the y-intercept of f(x) is 4 units above the y-intercept of g(x)

compare the function rule f(x) = log_2 (x + 1) and the graph of g(x). which statements are true?

g(x) increases at a faster rate for the interval [2, 3] f(x) and g(x) have the same rate for the interval [0, 1]

compare the function f(x) = x^2 - 4x + 5 with the following graph of g(x). which statement is true?

the minimum of f(x) is 2 more than the maximum of g(x)

ue the following graph of the function f(x) = 4 cos⁡(x), which passes through the approximate points a(−6, 3.84) and b(−4, −2.62), to answer the question. which is the average rate of change for the function f(x) over the interval −6≤ x ≤ −4?

-3.23

the graph shows the function f(x). what is the average rate of change for the function f(x) over the interval [0, 3]?

1.4

checkpoint 22

100%

unit 5 exam

100%

the graph shows the function g(x). https://cdstools.flipswitch.com/asset/media/1239958 what is the average rate of change for the function g(x) over the interval 0 ≤ x ≤ 4?

3.75

consider the function. f(x) = 4 log (x + 2) which interval has the smallest average rate of change in the given function?

5 < x < 7

lesson 23

compare average rates of change

lesson 21

compare intercepts

lesson 22

compare maxima and minima

examine the graphs of the two functions. https://cdstools.flipswitch.com/asset/media/1239962 based on the graphs of the two functions, which statement is true?

f(4) = g(4)

examine the graphs of the two functions. https://assets.learnosity.com/organisations/625/e6debcd5-4d37-4e7a-8440-59ef0990ab13.png based on the graphs of the two functions, which statement is true?

f(3) = g(3)

compare the function tule of f(x) = 2^x - 3 and the graph of g(x). which statement is true about f(x) and g(x) and their rates of change for the interval 0 < x < 3?

the rate of change for f(x) is faster than the rate of change for g(x)

compare the function 2^x+3 - 2 with the following graph of g(x). which statement about the y-intercept is true?

the y-intercept of f(x) is 2 units above the y-intercept of g(x).

use the table to calculate the average rate of change of f(x) over the interval [0, 4].

60

the table shows different values for functions f(x) and g(x), which are continuous for all x ≥ 0. over which intervals does f(x) = g(x)? select all that apply.

[2, 3] [5, 6]

consider the following function. f(x) = log_2 (x + 3) which interval has the smallest average rate of change in the given function?

[6, 8]

examine the graphs of the two functions. https://assets.learnosity.com/organisations/625/5bb0284d-e53b-44e0-8bd8-db69e3b9b7bb.png based on the graphs of the two functions, which statement is true?

f(0) = g(0)

examine the graphs of the two functions. https://cdstools.flipswitch.com/asset/media/1239961 based on the graphs of the two functions, which statement is true?

f(1) = g(1)

examine the graphs of the two functions. https://cdstools.flipswitch.com/asset/media/1239963 based on the graphs of the two functions, which statement is true?

f(1) = g(1)

examine the graphs of the two functions. https://assets.learnosity.com/organisations/625/1ba18a84-2c3f-4fa9-ae44-49355fb2853c.png based on the graphs of the two functions, which statement is true?

f(2) = g(2)

examine the table for f(x) and the graph of g(x). both are cubic functions. which statement about the x-intercepts is true?

f(x) and g(x) have two x-intercepts in common

examine the table for f(x) and the graph of g(x). both are quadratic functions. which two statements are true for f(x) and g(x)?

f(x) and g(x) share the x-intercept at (3, 0) the y-intercept of f(x) is above the y-intercept of g(x)

examine the table for f(x) and the graph for g(x). which statement is true for f(x) and g(x) over the interval 0 ≤ x ≤ 4?

f(x) increases at a faster rate

examine the table for f(x) and the graph for g(x). both are exponential functions. over the x-value interval [0, 2], which statements are true for the extrema of f(x) and g(x)?

the local minimum of f(x) is 3 more than the local minimum of g(x) the local maximum of f(x) is 19 more than the local maximum of g(x)

compare the function f(x) = √x+3 - 4 with the following graph of g(x). which statement about the extrema for f(x) and g(x) is true?

the minimum of f(x) is 2 less than the minimum of g(x)

examine the table for f(x) and the graph of g(x). both represent quadratic functions. which statements are true?

the y-intercept of f(x) is below the y-intercept of g(x) the x-intercepts of g(x) are between the x-intercepts of f(x)

compare the function f(x) = x^2 + 10x + 25 with the following graph of g(x). which statements are true? select all that apply.

the y-intercept of f(x) is greater than the y-intercept of g(x) the x-intercept of f(x) is to the left of the x-intercepts of g(x)

lesson 24

when f(x) = g(x)

compare the function rule f(x) = -x^2 + 4x + 3 and the graph of g(x). which statement is true about f(x) and g(x) and their rates of change for the interval [0, 3]?

f(x) increases at a faster rate

compare the graph of f(x) and the table of g(x). which two statements are true about f(x) and g(x) and the intervals [0, 2] and [2, 4]?

f(x) increases at a faster rate over the interval [2, 4] g(x) increase at a faster rate over the interval [0, 2]

examine the table for f(x) and the graph for g(x). both represent radical functions. which statement about the minimums for f(x) and g(x) is true?

the minimum of f(x) is 3 less than the minimum of g(x)

compare the function f(x) = 3x^2 - 12x + 10 with the following graph of g(x). which statement about the extrema of the functions is true?

the minimum of f(x) is 5 less than the minimum of g(x)

examine the table for f(x) and the graph for g(x). both represent quadratic functions. which statement about the vertices of the functions is true?

the minimum of f(x) is 6 more than the minimum of g(x)

examine the table for f(x) and the graph for g(x). both represent radical functions. which statement about the extrema for f(x) and g(x) is true?

the minimum value of f(x) is 11 more than the minimum value of g(x)

compare the function f(x) = 2^x + 3 with the following graph of g(x). over the x-value interval [-1, 2], which two statements are true for the extrema of f(x) and g(x)?

the relative maximum of f(x) is 2 more than the relative maximum of g(x) the relative minimum of f(x) is 5.5 more than the relative minimum of g(x)

compare the function f(x) = (x - 2)(x - 1)(x + 3) with the following graph of g(x). which two statements about the relative extrema of each function are true?

the relative minimum of f(x) is less than the relative minimum of g(x) the relative maximum of f(x) is more than the relative maximum of g(x)

compare the function f(x) = √x+6 − 4 with the following graph of g(x). which statement about the x-intercepts for f(x) and g(x) are true?

the x-intercept of f(x) is 15 units to the right of the x-intercept of g(x)

compare the function f(x) = √x+2 − 1 with the following graph of g(x). which statement about the x-intercepts for f(x) and g(x) is true?

the x-intercept of f(x) is 2 units to the left of the x-intercept of g(x).

examine the table for f(x) and the graph of g(x). both are radical functions. which statement for f(x) and g(x) is true?

the x-intercept of f(x) is 2 units to the right of the x-intercept of g(x)

examine the table for f(x) and the graph for g(x). both represent radical functions. which statements are true for f(x) and g(x)?

the y-intercept of f(x) is 3 units above the y-intercept of g(x) the x-intercept of f(x) is 15 units to the left of the x-intercept of g(x)

compare the function f(x) = (x - 2)(x - 1)(x + 3) with the following graph of g(x). which statements about the relative extrema of the functions are true? select two that apply.

the relative maximum of f(x) is more than the relative maximum of g(x) the relative minimum of f(x) is greater than the relative minimum of g(x)

examine the table for f(x) and the graph of g(x). both are exponential functions. which two statements are true for f(x) and g(x)?

the y-intercept of f(x) is below the y-intercept of g(x) the x-intercept of f(x) is the same as the x-intercept of g(x)

compare the function f(x) = 2^x+2 with the following graph of g(x). over the x-value interval [0, 3], which statements are true for the extrema of f(x) and g(x)?

the relative minimum of f(x) is 6 more than the relative minimum of g(x) the relative maximum of f(x) is 27 more than the relative maximum of g(x)

a nature conservation organization tracks the population of an endangered species of foxes over time. the population number is modeled by the function f(x) = −1.2^0.7x + 10,000, where x represents the time in years since the organization began tracking the foxes. over which time interval did the population decline the fastest?

[60, 70]

compare the function f(x) = (x − 1)(x + 2)(x + 3) with the following graph of g(x). which statement about the x-intercepts is true?

f(x) and g(x) have one x-intercept in common.

compare the function f(x) = (x + 1)(x − 2)(x + 3) with the following graph of g(x). which statement about the x-intercepts is true?

f(x) and g(x) have two x-intercepts in common

compare the function f(x) = (x - 1)(x - 2)(x + 4) with the following graph of g(x). which statement about the x-intercepts is true?

f(x) and g(x) have two x-intercepts in common

examine the table for f(x) and the graph of f(x). both are exponential functions. which two statements are true for f(x) and g(x)?

f(x) does not have an x-intercept the y-intercept of f(x) is 6 units above the y-intercept of g(x)

examine the table for f(x) and the graph of g(x). both represent radical functions. which statements are true for f(x) and g(x)?

the y-intercept of f(x) is about 2 units above the y-intercept of g(x). the x-intercept of f(x) is 3 units to the left of the x-intercept of g(x)

examine the table for f(x) and the graph for g(x). both represent exponential functions. which two statements are true for f(x) and g(x)?

the y-intercept of f(x) is above the y-intercept of g(x) the x-intercept of f(x) is 2 units to the right of the x-intercept of g(x)