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Eleventh Grade (Grade 11) Function and Algebra Concepts Questions

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Grade 11 Functions and Relations CCSS: HSF-BF.A.1, HSF-BF.A.1c
Given f(x)=ex and g(x) = ln x, what is (f∘g)(e²)?
  1. e2
  2. 2
  3. ee2
  4. ln 2
Grade 11 Functions and Relations CCSS: HSF-BF.A.1, HSF-BF.A.1c
For f(x)=1x and g(x) = x − 1, the domain of (g∘f)(x) is__.
  1. x ≠ 0
  2. x ≠ 1
  3. All real numbers
  4. x > 0
Grade 11 Functions and Relations CCSS: HSF-BF.A.1, HSF-BF.A.1c
If f(x) = √x and g(x) = x², what is (g∘f)(4)?
  1. 2
  2. 4
  3. 16
  4. 8
Grade 11 Functions and Relations CCSS: HSF-BF.B.4, HSF-BF.B.4d
The graph is plotted for Plot y=x4-8x2.
Which restriction makes it invertible?
  1. x ≥ 2
  2. x ≤ -2
  3. -2 ≤ x ≤ 0
  4. All of the above
Grade 11 Functions and Relations CCSS: HSF-BF.B.4, HSF-BF.B.4d
The graph is plotted for y = ln(x - 2).
If restricted to `x > 3`, what is the inverse?
  1. y=ex+2
  2. y=ex-2
  3. y=ex-2
  4. y=ex+2
Grade 11 Functions and Relations CCSS: HSF-BF.B.4, HSF-BF.B.4d
Given f(x)=10−x3 Which domain makes f(x) invertible?
  1. x ≥ 0
  2. x ≤ 0
  3. No restriction needed
  4. x > 10
Grade 11 Functions and Relations CCSS: HSF-BF.B.4, HSF-BF.B.4d
Given f(x) = ln(x + 4) Which domain makes f(x) invertible?
  1. x > −4
  2. x ≤ −4
  3. x ≥ 0
  4. x ≠ −4
Grade 11 Functions and Relations CCSS: HSF-BF.B.4, HSF-BF.B.4d
Why is this restricted function invertible?
  1. It passes the vertical line test
  2. It's one-to-one on this domain
  3. It's always increasing
  4. Both A and B
Grade 11 Functions and Relations CCSS: HSF-BF.B.4, HSF-BF.B.4d
Given f(x)=−2(x+3)2+5 Which domain makes f(x) invertible?
  1. x ≤ −3
  2. x ≥ 0
  3. x > −3
  4. x ≤ 5
Grade 11 Functions and Relations CCSS: HSF-BF.B.4, HSF-BF.B.4d
The graph is plotted for y = -cos(x).
What restriction matches cos⁻¹(x)'s domain?
  1. [0, π]
  2. [-π2,π2]
  3. [-π, 0]
  4. [π, 2π]
Grade 11 Functions and Relations CCSS: HSF-BF.B.4, HSF-BF.B.4d
Is the combined function invertible?
  1. Yes
  2. No
  3. Only if restricted further
  4. Only for x > 1
Grade 11 Functions and Relations CCSS: HSF-BF.B.4, HSF-BF.B.4d
The graph is plotted for y=x3-4x.
Which domain restriction would NOT make it invertible?
  1. x ≥ 2
  2. x ≤ -2
  3. -1 ≤ x ≤ 1
  4. x ≥ 0
Grade 11 Functions and Relations CCSS: HSF-BF.B.4, HSF-BF.B.4d
The graph is plotted for y = 2sin(x).
What is the standard restricted domain for creating sin⁻¹(x)?
  1. [0, π]
  2. [-π, π]
  3. [-π2,π2]
  4. [0, 2π]
Grade 11 Functions and Relations CCSS: HSF-BF.B.4, HSF-BF.B.4d
The graph is plotted for y=x4-4x2unrestricted.
Which domain restriction would NOT make it invertible?
  1. x ≥ √2
  2. x ≤ -√2
  3. -√2 ≤ x ≤ 0
  4. 0 ≤ x ≤ √2
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