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Functions and Relations Questions - All Grades

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Grade 9 Functions and Relations CCSS: HSF-IF.A.1
Grade 11 Functions and Relations CCSS: HSF-BF.B.4, HSF-BF.B.4a
Find the inverse of the following function. [math]f(x) = 4x^3 + 2[/math]
  1. [math]f^{-1}(x) = (x^3-2)/4[/math]
  2. [math]f^{-1}(x) = (root[3](x) - 2)/4[/math]
  3. [math]f^{-1}(x) = root[3]((x-2)/4) [/math]
  4. [math]f^{-1}(x) = root[3](x-2)/4[/math]
Grade 11 Functions and Relations CCSS: HSF-BF.A.1, HSF-BF.A.1b
Find the function [math](f/g)(x)[/math] and its domain if [math]f(x) = sqrt(-x)[/math] and [math]g(x) = sqrt(x+5)[/math].
  1. [math](-x)/(x+5); \ \ -5 < x <= 0[/math]
  2. [math](-x)/(x+5); \ \ x!=-5[/math]
  3. [math]sqrt((-x)/(x+5)); \ \ -5 < x <= 0[/math]
  4. [math]sqrt((-x)/(x+5)); \ \ x <-5 or x >= 0[/math]
Grade 10 Functions and Relations CCSS: HSF-BF.B.4, HSF-BF.B.4a
Find the inverse of the function [math]f(x) = 3x-2[/math].
  1. [math]f^{-1}(x) = 1/3 x + 2[/math]
  2. [math]f^{-1}(x) = x +2 [/math]
  3. [math]f^{-1}(x) = x + 2/3[/math]
  4. [math]f^{-1}(x) = 1/3 x + 2/3[/math]
Grade 8 Functions and Relations CCSS: 8.F.A.3
Is this graph linear?
Graph - Linear Function y=-2x
  1. Yes
  2. No
  3. Not enough information
  4. Sometimes
Grade 9 Functions and Relations CCSS: HSF-LE.A.1, HSF-LE.A.1a
A function which has a constant difference per interval is
  1. linear.
  2. exponential.
  3. logarithmic.
  4. none of the above.
Grade 11 Functions and Relations CCSS: HSF-BF.B.4, HSF-BF.B.4a
Find the inverse. [math]f(x) = (x-8)/(x+1)[/math]
  1. [math]f^{-1}(x) = (x-1)/(x+8)[/math]
  2. [math]f^{-1}(x) = -9/(x+1)[/math]
  3. [math]f^{-1}(x) = (-x-8)/(x-1)[/math]
  4. [math]f^{-1}(x) = (x-8)/x[/math]
Grade 10 Functions and Relations CCSS: HSF-IF.A.1
If the domain of the function [math]f(x) = 5x^2 - 3[/math] is restricted to the values [math]{2,4,6,8}[/math], what is the range of this function?
  1. [math]RR[/math]
  2. [math]{17, 77, 177, 317}[/math]
  3. [math]{2,4,6,8}[/math]
  4. [math]{x in RR | x >=-3}[/math]
Grade 8 Functions and Relations CCSS: 8.F.A.3
The equation [math]y=-2x^2+2[/math] is
  1. linear.
  2. nonlinear.
  3. not a function.
  4. both b and c.
Grade 8 Functions and Relations CCSS: 8.F.A.3
Is this graph linear?
Graph - Quadratic Function y=-1/2x^2
  1. Yes
  2. No
  3. Not enough information
  4. Sometimes
Grade 10 Functions and Relations CCSS: HSF-IF.A.1
Is the following a function? Explain why or why not.
Coordinate Plane - 5x5 - With Dots
  1. Yes, this does represent a function, because all the points are distinct (none of them are coincident).
  2. No, this does not represent a function, since a function can not be made up of only points.
  3. No, this does not represent a function, since it fails the vertical line test.
  4. No, this does not represent a function, since a function is made up of many more points.
Grade 10 Functions and Relations CCSS: HSF-IF.B.5
For the function pictured below, with endpoints at [math]x=0[/math] and [math]x=10[/math], what is the range of this function? Assume 1 unit intervals for both axes.
Graph - Piecewise Random 1
  1. [math]RR[/math]
  2. [math]{y in RR | y >= 0 and y <= 10}[/math]
  3. [math]{y in RR | y >= 0 and y <=4}[/math]
  4. [math]{y in RR | y >= 0}[/math]
Grade 11 Functions and Relations CCSS: HSF-IF.C.7, HSF-IF.C.7d
Grade 11 Functions and Relations CCSS: HSF-IF.C.7, HSF-IF.C.7c
When graphing a polynomial function of degree 8, whose leading coefficient is -3, which of the following is correct?
  1. The function tends toward positive infinity as x approaches negative and positive infinity.
  2. The function tends toward negative infinity as x approaches negative and positive infinity.
  3. The function tends toward negative infinity as x approaches negative infinity, and the function tends toward positive infinity as x approaches positive infinity.
  4. The function tends toward positive infinity as x approaches negative infinity, and the function tends toward negative infinity as x approaches positive infinity.
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