Composition and Inverse Functions 25/26 hisd

Orville composed functions f(x) = ³√(x) - 2 and g(x) = ((x+2)/4)³ to see if the two functions are inverses of each other. His work is shown below: f ∘ g = f(g(x)) f ∘ g = f(((x+2)/4)³) f ∘ g = ³√((x+2)/4)³ - 2 f ∘ g = ((x+2)/4) - 2 f ∘ g = (x+2-8)/4 f ∘ g = (x-6)/4 Which of the following is true about Orville’s work? Select THREE correct answers.

• Orville’s work is not correct.

• Orville’s work indicates that the functions are inverses.

• Orville’s work is correct.

• Orville’s work indicates that the functions are not inverses.

• The two functions f and g are not inverses.

Tags

CCSS.HSF-BF.B.4B

Casey is trying to determine whether the two functions f and g are inverses. She composes f with g, generating the graph shown, where f and g are shown as solid blue lines and f(g(x)) is shown as a dashed red line.

• f and g are inverse functions because f ∘ g represents the identity functions.

• The graph of f can be reflected over the line f(g(x)) to generate the graph of g.

• The graph of f(g(x)) indicates that f and g are NOT inverses of each other.

• The graph of f(g(x)) does not provide enough information for Casey to draw a conclusion.

Tags

CCSS.HSF-BF.B.4B

Which of the following graphs represents y as a function of x where y is the distance from -2?

• [Graph A]

• [Graph B]

• [Graph C]

• [Graph D]

Tags

CCSS.HSF-IF.C.7D

What is the range of f(x) = |x| + 4, shown in the graph?

• { y | y > 4 }

• { y | y ≥ 4 }

• { y | y < 4 }

• { y | y ≤ 4 }

Tags

CCSS.8.F.A.1

CCSS.HSF.IF.B.5

Zeke draws a graph of m(x) = 3|x + 4|. Select the THREE statements that are correct.

• m(x) has an axis of symmetry at x = -4.

• m(x) represents 3 times the distance, x, from -4.

• m(x) is increasing over the interval (-4, ∞).

• m(x) has a y-intercept at (0, -4).

• m(x) is decreasing over the interval (-∞, 4).

Which of the following does NOT correctly describe the absolute value parent function?

• The function has an axis of symmetry at x = 0, so it can be reflected over x = 0 without changing.

• The function has a vertex at (0, 0).

• The function is defined for all real numbers.

• The function increases over the interval (-∞, 0) and decreases over the interval (0, ∞).

Tags

CCSS.HSF-IF.C.7D

Estefani is designing the manufacturing that will produce packing material for a particular computer chip. The packing material needs to be within 0.8 mm of the desired thickness, which is 18.0 mm. Which equation can Estefani use to represent the limits of the width, w, of the packing material?

• |0.8 - w| = 18.0

• |18.0 - w| = 0.8

• |18.0 + w| = 0.8

• |0.8 + w| = 18.0

Tags

CCSS.HSA.CED.A.3

Björn took a poll for an upcoming local election and found that 27% of voters were likely to vote for the incumbent. His poll has a 4% margin of error. Which of the following equations represents the likely minimum and maximum percentages of voters, v, that will vote for the incumbent? Choose TWO correct answers

• |4 - v| = 27

• |27 - 4| = v

• |27 - v| = 4

• |v - 27| = 4

• |4 - 27| = v

Tags

CCSS.HSA.CED.A.3

Leah owns an apple orchard and allows customers to walk the orchard and pick their own apples. • Leah charges $30 for a bushel of self-picked apples. • She knows that a typical bushel of the apples from her orchard weighs about 19 kilograms and wants to make sure she doesn’t overcharge or undercharge people, so she weighs each bushel before allowing it to be purchased. What does the equation |19 - x| = 2 represent in this scenario?

• If a bushel of apples weighs less than 19 kilograms, Leah grants a 2-dollar discount.

• The maximum difference between 19 kilograms and the weight of a bushel of apples Leah sells should be 2 kilograms.

• A bushel of apples that a customer purchases from Leah should be 19 + 2 kilograms.

• The maximum difference between 2 kilograms and the weight of a bushel of apples Leah sells should be 19 kilograms.

Tags

CCSS.HSA.CED.A.3

Based on the table above, what is the value of y when x = 4?

• 4

• 0

• 2

• 6

• -2

Tags

CCSS.8.F.A.1

CCSS.HSF.IF.A.1