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Tenth Grade (Grade 10) Functions and Relations Questions

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Grade 10 Functions and Relations CCSS: HSF-IF.C.9

For what values of the domain is the function

$f(x)= 2x-2$ less than the function represented in the graph?
Graph - Linear Function y=2x

All real numbers
$x > 0$
$-1 < x < 0$
$-2 < x$

Grade 10 Functions and Relations CCSS: HSF-IF.C.9

For what values of

$x$ is the function

$f(x)= 2x^2+2$ greater than the function presented in the graph?
Graph - Quadratic Function y=1/2x^2

All real numbers
$x = 0$
$-1 < x < 1$
Never

Grade 10 Functions and Relations CCSS: HSF-BF.A.1, HSF-BF.A.1a

Determine the function rule which models the data from the table.

$\ \ \ \ \ \ \ \ \ mathbf{x} \ \ \ \ \ \ \ \ \$	$\ \ \ \ \ \ -2 \ \ \ \ \ \$	$\ \ \ \ \ \ -1 \ \ \ \ \ \$	$\ \ \ \ \ \ 0 \ \ \ \ \ \$	$\ \ \ \ \ \ 1 \ \ \ \ \ \$	$\ \ \ \ \ \ 2 \ \ \ \ \ \$
$\ \ \ \ \ \ \ \ \ \mathbf{f(x)} \ \ \ \ \ \ \ \ \$	$-45$	$-25$	$-5$	$15$	$35$

$f(x) = 20x - 5$
$f(x) = -1/2 x^2 + 37.2 x - 6$
$f(x) = -20x - 5$
$f(x) = 20x$

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

It is raining where Sarah lives, and she is watching a cup that is outside fill with water. Every ten minutes, the water level is 1 cm higher. Which type of function would best describe the increasing water level over time?

Linear
Exponential
Square root
None of the above

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

What is the value of

$c$ , if

$g(s) = 6s-9$ and

$g(c) = -21 ?$

-2
-21
5
-135

Grade 10 Functions and Relations CCSS: HSF-IF.C.9

$g(x)$ is a linear function, some of whose values are listed in the table below, and

$f(x) = 3x-2$ , which of the following is/are true? There may be more than one correct answer.

$\ \ \ \ \ \ \ \ \ mathbf{x} \ \ \ \ \ \ \ \ \$	$\ \ \ \ \ \ \ \ \ \mathbf{g(x)} \ \ \ \ \ \ \ \ \$
$-2$	$-3$
$-1$	$-5/2$
$0$	$-2$
$1$	$-3/2$
$2$	$-1$
$3$	$-1/2$
$4$	$0$
$5$	$1/2$

Both functions have the same slope.
Both functions have a y-intercept of -2.
Both functions have an x-intercept of 2/3.
If graphed, both functions would have values in quadrants I, III, and IV.

Grade 10 Functions and Relations CCSS: HSF-IF.C.9

Given two linear functions,

$f(x)$ which has some of its values listed in the table and

$g(x)$ represented graphically, determine which function has a greater slope. If the slopes are equal, determine whether the lines are coincident or not. Let

$m_f$ represent the slope of function

$f$ and

$m_g$ represent the slope of function

$g$ .

$\ \ \ \ \ \ \ \ \ mathbf{x} \ \ \ \ \ \ \ \ \$	$\ \ \ \ \ \ \ \ \ \mathbf{f(x)} \ \ \ \ \ \ \ \ \$
$-2$	$7$
$-1$	$4$
$0$	$1$
$1$	$-2$
$2$	$-5$

$m_f > m_g$
$m_f < m_g$
$m_f = m_g$ The lines are not coincident.
$m_f = m_g$ The lines are coincident.

Grade 10 Functions and Relations CCSS: HSF-IF.A.3

The third, fourth, and fifth numbers in a sequence are

$16, 22, 28$ . Which function describes the sequence?

$f(n)=6n+16$
$f(n)=6n-2$
$f(x)=3x+12$
$f(x)=12x+6$

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

For the function

$f(x) = 3x^2 - x^-1$ , which of the following are equal?

__	$f(1)$	A.	$23/2$
__	$f(2)$	B.	$25/2$
__	$f(-1)$	C.	$4$
__	$f(-2)$	D.	$2$

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

Given the table below, which of the following function rules defines this relationship?

$\ \ \ \ \mathbf{x} \ \ \ \$	$\ \ \ \ \mathbf{f(x)} \ \ \ \$
$-2$	$23$
$-1$	$2$
$0$	$-1$
$1$	$-4$
$2$	$-25$

$f(x) = -8x + 5$
$f(x) = -3x^3 -1$
$f(x) = -3x^2 - 2$
$f(x) = -2x^4 - 8$

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

Find the value of

$h(4)$ if

$h(t) = -2t^3 + 7t^2 + 9$ .

-7
4
113
249

Grade 10 Functions and Relations CCSS: HSF-IF.C.7, HSF-IF.C.7b

When graphing a square root function of the form

$f(x) = a sqrt(bx + c) +d$ , where

$a,b,c,d in RR$ , there is always either a minimum or maximum value (but not both).

True
False

Grade 10 Functions and Relations CCSS: HSF-IF.A.3

Which function describes the sequence

$3, 7, 11...$ ?

$f(n)=4n-1$
$f(n)=3+2n$
$f(x)=2n-3$
$f(n)=4x-1$

Grade 10 Functions and Relations CCSS: HSF-IF.B.6

A small shop at the mall wraps presents during the holidays. Over the past few years, they have kept track of the number of workers they have on hand and the number of presents they are able to wrap in an hour. The following table represents this data.

$\ \ \ \ "Number of Workers" \ \ \ \$	$\ \ \ \ "Number of Presents Wrapped per Hour" \ \ \ \$
$5$	$24$
$6$	$28$
$7$	$33$
$8$	$40$
$9$	$44$
$10$	$46$

If this year they currently have 7 workers, what would be the most productive number of additional employees to hire, and why?

0, because they are already wrapping presents as efficiently as they can.
3, since this would mean the most presents wrapped in an hour.
2, since this would be the largest average increase possible (the most additional presents wrapped for each worker hired).
1, because this would be the largest average increase possible (the most additional presents wrapped for each worker hired).

Grade 10 Functions and Relations

Express the following interval using set-builder notation.

$[10,15)$

${x| 10 < x <15}$
${x| 10<=x<15}$
${x| 10 <= x <=15}$
${x| 10 < x <=15}$

Grade 10 Functions and Relations CCSS: HSF-IF.B.5

A bakery makes cookies and sells them for $2.00 each. The revenue the bakery makes from selling cookies is modeled by a function, where the input of the function is how many cookies the bakery makes. Which of the following would be the most appropriate domain for this function?

The set of all integers.
The set of positive integers and zero.
The set of even numbers.
The set of real numbers from 1 to 1,000.

Grade 10 Functions and Relations CCSS: HSF-IF.B.4

Which of the following statements about inverse functions is true?

Every function has an inverse.
Every inverse function is also a function.
The graph of a function and its inverse are always mirror images of each other.
The composition of a function and its inverse is the identity function.

Grade 10 Functions and Relations CCSS: HSF-IF.B.5

Shawn is filling a 5 L bottle with water. As the water increases, so does the weight of the bottle. This can be modeled by a function, where the input is how much water has been put into the barrel in liters. Which of the following would be the most appropriate domain for this function?

The set of all real numbers.
The set of integers numbers.
The set of integers numbers, from 0 to 5.
The set of all real numbers, from 0 to 5.

Grade 10 Functions and Relations CCSS: HSF-IF.B.4

Which of the following is the domain of the function

$f(x) = 1/(x - 2)$ ?

All real numbers
All real numbers except x = 2
All real numbers except x = -2
All real numbers except x = $1/2$

Grade 10 Functions and Relations CCSS: HSF-IF.B.6

What is the average rate of change between

$x=-1$ and

$x=2$ for the following function? Assume 1 unit intervals for both axes.

$1/6$
$3/2$
$2/3$
$0$

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Tenth Grade (Grade 10) Functions and Relations Questions