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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. $f(x) = 4x^3 + 2$
1. $f^{-1}(x) = (x^3-2)/4$
2. $f^{-1}(x) = (root[3](x) - 2)/4$
3. $f^{-1}(x) = root[3]((x-2)/4)$
4. $f^{-1}(x) = root[3](x-2)/4$
Grade 11 Functions and Relations CCSS: HSF-BF.A.1, HSF-BF.A.1b
Find the function $(f/g)(x)$ and its domain if $f(x) = sqrt(-x)$ and $g(x) = sqrt(x+5)$.
1. $(-x)/(x+5); \ \ -5 < x <= 0$
2. $(-x)/(x+5); \ \ x!=-5$
3. $sqrt((-x)/(x+5)); \ \ -5 < x <= 0$
4. $sqrt((-x)/(x+5)); \ \ x <-5 or x >= 0$
Grade 10 Functions and Relations CCSS: HSF-BF.B.4, HSF-BF.B.4a
Find the inverse of the function $f(x) = 3x-2$.
1. $f^{-1}(x) = 1/3 x + 2$
2. $f^{-1}(x) = x +2$
3. $f^{-1}(x) = x + 2/3$
4. $f^{-1}(x) = 1/3 x + 2/3$
Grade 8 Functions and Relations CCSS: 8.F.A.3
Is this graph linear?
1. Yes
2. No
3. Not enough information
4. Sometimes
Grade 8 Functions and Relations CCSS: 8.F.B.5
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 8 Functions and Relations CCSS: 8.F.B.5
Grade 11 Functions and Relations CCSS: HSF-BF.B.4, HSF-BF.B.4a
Find the inverse. $f(x) = (x-8)/(x+1)$
1. $f^{-1}(x) = (x-1)/(x+8)$
2. $f^{-1}(x) = -9/(x+1)$
3. $f^{-1}(x) = (-x-8)/(x-1)$
4. $f^{-1}(x) = (x-8)/x$
Grade 8 Functions and Relations CCSS: 8.F.B.4
Grade 10 Functions and Relations CCSS: HSF-IF.A.1
If the domain of the function $f(x) = 5x^2 - 3$ is restricted to the values ${2,4,6,8}$, what is the range of this function?
1. $RR$
2. ${17, 77, 177, 317}$
3. ${2,4,6,8}$
4. ${x in RR | x >=-3}$
Grade 8 Functions and Relations CCSS: 8.F.A.3
The equation $y=-2x^2+2$ 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?
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.
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 $x=0$ and $x=10$, what is the range of this function? Assume 1 unit intervals for both axes.
1. $RR$
2. ${y in RR | y >= 0 and y <= 10}$
3. ${y in RR | y >= 0 and y <=4}$
4. ${y in RR | y >= 0}$
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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