Back to Tutor Intake Assessment: Functions

8.F Tutor Intake — Functions: Define, Compare, and Model

This short check helps your tutor understand where to start. Answer each question without help. If you're not sure, give your best try — the goal is to find what to work on together, not to grade you.

Grade 8·13 problems·~13 min·Common Core Math - Grade 8·domain·f

Work through problems with immediate feedback

Concepts

A function is a rule that assigns to each input exactly one output.
Which of the following relationships, given as a set of (input, output)
pairs, is NOT a function?

{(1, 4), (2, 7), (3, 4), (5, 9)}

{(0, 5), (1, 5), (2, 5), (3, 5)}

{(2, 3), (4, 6), (2, 8), (5, 1)}

{(1, 2), (3, 6), (4, 8), (6, 12)}

A student claims the table below is NOT a function because the
output 10 appears more than once.

Input (x)	Output (y)
1	10
2	14
3	10
4	18

Is the student correct, and why?

No — the table IS a function. Each input has exactly one output;
two different inputs sharing the output 10 is allowed.

Yes — it is not a function because the output 10 is repeated for
inputs 1 and 3.

No — the table IS a function only because all the inputs are
different; if any output repeated it would fail.

Yes — it is not a function because the outputs are not all
different from one another.

$A circle centered at the origin on a coordinate plane.$

The graph shown is a circle on the coordinate plane. Using the
vertical line test, does this graph represent a function?

No — a vertical line drawn through the circle crosses it at two
points, so one input has two outputs.

Yes — a circle is a smooth closed curve, and smooth curves are
always functions.

Yes — every point on the circle has its own x-coordinate and
y-coordinate, so it is a function.

No — a circle is not a function because its graph is curved
rather than a straight line.

Classify the function shown in this table as linear or nonlinear.

x	y
0	2
1	5
2	10
3	17

Which statement is correct?

Nonlinear — the rate of change is not constant (the y-values
increase by 3, 5, 7).

Linear — the y-values keep increasing, so it is a straight line.

Nonlinear — it is not a function because the differences keep
changing.

Linear — the x-values increase by the same amount each row.

Which of these equations defines a LINEAR function?

$y = 3^{x}$

$y = x^{2} - 4$

$y = -2x + 7$

$y = \dfrac{6}{x}$

$A graph rising in a straight line in section A, flat in section B, and falling in a straight line in section C.$

The graph shows a quantity over time, divided into three sections
labeled A, B, and C. Which description correctly matches all three
sections?

A: increasing; B: constant; C: decreasing.

A: increasing; B: decreasing; C: constant.

A: positive; B: zero; C: negative (the value is negative in C).

A: decreasing; B: constant; C: increasing.

Procedures

The table below represents a linear function. Find the rate of change
(slope). Enter a number.

x	y
2	7
4	13
6	19
8	25

The table below represents a linear function. Find the initial value
(the output when x = 0). Enter a number.

x	y
3	20
4	24
5	28
6	32

A linear function passes through the points (2, 5) and (6, 17).
Find the rate of change (slope). Enter a number.

A linear function has rate of change m = 4 and passes through the
point (3, 14). What is its initial value b (the y-intercept)?

You're viewing 2 of 3 sections.

Create a free account to continue the full exercise set and save your progress.

Create free account

0 of 10 answered

Answer all problems to submit.