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Functions and Relations Questions - All Grades

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Grade 10 Functions and Relations CCSS: HSF-IF.A.2

Evaluate

$f(x) = -x + 5$ for

$x = -2$ .

$f(-2) = 7$
$f(-2) = 10$
$f(-2) = -7$
$f(-2) = 3$

Grade 9 Functions and Relations CCSS: HSF-IF.A.1

What is the domain of the set of ordered pairs?
(8, -13); ( 0, -5) ; (4, -9); (-3,2)

(-3, 0, 4, 8)
(-3, -2)
(-2, -5, -9, -13)
(-3, 8)

Grade 11 Functions and Relations CCSS: HSF-BF.B.4, HSF-BF.B.4a

Find the inverse of the following function.

$f(x) = 4x^3 + 2$

$f^{-1}(x) = (x^3-2)/4$
$f^{-1}(x) = (root[3](x) - 2)/4$
$f^{-1}(x) = root[3]((x-2)/4)$
$f^{-1}(x) = root[3](x-2)/4$

Grade 10 Functions and Relations CCSS: HSF-IF.A.1

Is the following a function? Explain why or why not.

Yes, this does represent a function, because all the points are distinct (none of them are coincident).
No, this does not represent a function, since a function can not be made up of only points.
No, this does not represent a function, since it fails the vertical line test.
No, this does not represent a function, since a function is made up of many more points.

Grade 9 Functions and Relations CCSS: HSF-LE.A.2

Some of the values of

$f(x)$ are given in the table below. What is the function rule for this linear function?

$\ \ \ \ \ \ \ \ \ \ \ mathbf{x} \ \ \ \ \ \ \ \ \ \ \$	$\ \ \ \ \ \ \ \ \ \ \mathbf{f(x)} \ \ \ \ \ \ \ \ \ \$
$0$	$2$
$1$	$-8$
$2$	$-18$
$3$	$-28$

$f(x) = 10x - 2$
$f(x) = -10x + 2$
$f(x) = 10x + 2$
$f(x) = -10x - 2$

Grade 11 Functions and Relations CCSS: HSF-BF.B.4, HSF-BF.B.4b

$f(x) = 1/(1+e⁻ˣ)$ and

$g(x) = ln(x/(1-2x))$ , are they inverses?

True
False

Grade 11 Functions and Relations CCSS: HSF-BF.B.4, HSF-BF.B.4b

For

$f(x) = (3 + ln(x+2))/(4 - ln(x+2))$ and

$g(x) = e^[(3-4x)/(x+1)] - 2,$ verify if g = f⁻¹.

True
False

Grade 11 Functions and Relations CCSS: HSF-BF.B.4, HSF-BF.B.4b

Given

$f(x) = 2^(3x-1) + 5$ and

$g(x) = [log_2(x-5)+1]/3$ , is g = f⁻¹?

True
False

Grade 11 Functions and Relations CCSS: HSF-BF.B.4, HSF-BF.B.4b

For

$f(x) = 5 - 3/(x+1)$ and

$g(x) = (3/(5-x)) - 1$ , verify inverse relationship.

True
False

Grade 11 Functions and Relations CCSS: HSF-BF.B.4, HSF-BF.B.4b

Given

$f(x) = (2eˣ-3)/(eˣ+4)$ and

$g(x) = ln[(3+4x)/(2-x)]$ , is g = f⁻¹?

True
False

Grade 11 Functions and Relations CCSS: HSF-BF.B.4b

Given f(x) = 3eˣ⁻² and

$g(x) = ln(x/3) + 2$ , is g the inverse of f?

True
False

Grade 11 Functions and Relations CCSS: HSF-BF.B.4b

For

$f(x) = 5 - e^(x+2)$ and g(x) = ln(5+x) - 2, verify if g = f⁻¹.

True
False

Grade 11 Functions and Relations CCSS: HSF-BF.B.4, HSF-BF.B.4b

For

$f(x) = (lnx + 1)/(lnx - 2)$ and

$g(x) = e^[(1+2x)/(x-1)]$ , verify inverse relationship.

True
False

Grade 11 Functions and Relations CCSS: HSF-BF.B.4b

Given f(x) = log(x²+1) and g(x) = √(10ˣ-1), is g = f⁻¹?

True
False

Grade 11 Functions and Relations CCSS: HSF-BF.B.4b

For

$f(x) = (4 - x)/(3x + 2)$ and

$g(x) = (4 - 2x)/(3x + 1)$ , verify inverse relationship.

Grade 11 Functions and Relations CCSS: HSF-BF.B.4b

$f(x) = (eˣ-3)/(eˣ+2)$ and

$g(x) = ln[(3+2x)/(1-x)]$ , are they inverses?

True
False

Grade 11 Functions and Relations CCSS: HSF-BF.B.4b

Given

$f(x) = (3x-2)/(x+1)$ and

$g(x) = (-x-2)/(x-3)$ , is g = f⁻¹?

True
False

Grade 11 Functions and Relations CCSS: HSF-BF.B.4b

Given f(x) = 5x + 2 and

$g(x) = (x - 2)/5$ , is g = f⁻¹?

Grade 11 Functions and Relations CCSS: HSF-BF.B.4b

Given

$f(x) = 2 + 1/(x-3)$ and

$g(x) = 2 + 1/(x-3)$ , are they inverses?

True
False

Grade 11 Functions and Relations CCSS: HSF-BF.B.4b

For

$f(x) = (x - 1)/(x + 4)$ and

$g(x) = (-4x - 1)/(x - 1)$ , verify if g = f⁻¹.

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Functions and Relations Questions - All Grades