Peak PeeperFunction Machines · functions, their graphs, and sequences

Spots the peaks, valleys and zeros of a graph: reading graphs of functions.

Reading Graphs of Functions

Reading graphs of functions. In MathBound, the free Algebra I adventure game, Peak Peeper asks these problems, and the only way past is to solve them.

Part of Functions: chapter 4 of the standard course.

Play this battle free

10 questions, no sign-up, nothing saved. Climbs from the basics to harder questions.

What you will practice

Intercepts and Zeros from a Graph. Read the y-intercept of a graphed line.
Key Features of a Graph. Read the maximum or minimum of a graph: a parabola, a V, a square root curve or straight pieces.
Solving with Graphs. Read a function value from its graph.

Worked examples

Made by the game’s own question engine. Try each one, then open its steps.

Example 1 · Solving with Graphs

The

table

gives

values

of

the

quadratic

function

f

and

the

linear

function

g .

For

which

values

of

x

is

f (x) = g (x)? x f (x) g (x) - 1 - 4 0 0221642863884610

$x = 3$ $only$
$x = 0$ $and$ $x = 3$
$x = 2$ $and$ $x = 8$
$x = 0$ $only$

Show the worked steps

$f (x) = g (x)$ $where$ $the$ $two$ $rows$ $of$ $the$ $table$ $hold$ $the$ $same$ $number.$
$f (0) = g (0) = 2$ $and$ $f (3) = g (3) = 8. f (x) - g (x)$ $is$ $a$ $quadratic,$ $which$ $has$ $at$ $most$ $two$ $zeros,$ $so$ $x = 0$ $and$ $x = 3 .$

Answer: $x = 0$ $and$ $x = 3$

Example 2 · Intercepts and Zeros from a Graph

The

table

shows

values

of

a

quadratic

function

f .

What

are

the

zeros

of

f ? x f (x) - 5 5 - 4 0 - 3 - 3 - 2 - 4 - 1 - 3 0015

$x = - 4$
$x = 0$ $and$ $x = 4$
$x = - 4$ $and$ $x = 0$
$x = - 2$

Show the worked steps

$A$ $zero$ $is$ $an$ $x -value$ $where$ $f (x) = 0.$
$f (x) = 0$ $at$ $x = - 4$ $and$ $at$ $x = 0,$ $so$ $x = - 4$ $and$ $x = 0 .$

Answer: $x = - 4$ $and$ $x = 0$

Example 3 · Intercepts and Zeros from a Graph

The

table

shows

values

of

a

quadratic

function

f .

Between

which

two

consecutive

integers

is

the

greater

zero

of

f ? x f (x) - 1 2 0 - 3 1 - 6 2 - 7 3 - 6 4 - 3 52

$between$ $5$ $and$ $6$
$between$ $4$ $and$ $5$
$between$ $- 1$ $and$ $0$
$between$ $3$ $and$ $4$

Show the worked steps

$A$ $zero$ $lies$ $where$ $f (x)$ $changes$ $sign$ $between$ $two$ $columns$ $of$ $the$ $table .$
$f (4) = - 3$ $and$ $f (5) = 2$ $have$ $opposite$ $signs,$ $so$ $the$ $greater$ $zero$ $is$ $between$ $4$ $and$ $5 .$

Answer: $between$ $4$ $and$ $5$

Where it is in your textbook

Textbook	Lessons
Standard course	4.3, 4.7, 6.1, 9.6
Big Ideas Math Algebra 1	3.3, 5.1, 5.5, 8.1, 8.2, 9.2, 9.6
Big Ideas Math Algebra 1 (2022)	3.2, 3.4, 5.1, 5.5, 8.1, 8.2, 9.2, 9.6
Carnegie Learning Algebra I	M1 1.1, M1 1.2, M1 1.4, M2 4.4, M3 2.2, M5 1.1, M5 1.2, M5 3.1, M5 3.2
CPM Core Connections Algebra	1.1.3, 1.2.1, 1.2.5, 2.2.3, 7.2.3, 8.2.1, 10.3.1, 11.3.3
CPS Skyline Algebra	3.1-3.3, 3.4, 3.6, 6.4, 8.3-8.4
enVision Algebra 1	5-1, 9-1, 10-3
enVision Algebra 1 (2024)	5-1, 9-1, 10-3
Eureka Math Algebra I (EngageNY)	1.1-1.3, 1.4-1.5, 3.11-3.13, 3.15-3.16, 4.8-4.10, 4.22, 5.1, 5.4
Glencoe Algebra 1	1-8, 3-2, 6-1, 9-1, 9-2
HMH Into Algebra 1	4.3, 17.1, 19.4, 20.3
Holt McDougal Larson Algebra 1	1.8, 3.5 Ext, 4.7, 6.1, 9.1, 9.3, 9.7
Illustrative Mathematics Algebra 1	4.1-4.3, 4.6, 4.7-4.9, 4.10-4.11, 5.11-5.13, 7.1-7.2
Illustrative Mathematics Algebra 1 (v.360)	5.1-5.3, 5.6, 5.7-5.9, 5.10-5.11, 6.11-6.13, 8.1-8.2
Math Nation Algebra 1 (Florida B.E.S.T.)	1.2, 4.2, 4.7, 5.7, 8.1, 8.2, 8.9, 9.2, 10.1, 10.2, 13.3
MVP Mathematics I (Integrated Math 1)	2.8, 3.1, 3.2, 3.3, 3.5
Open Up NC Math 1 (MVP)	2.6, 3.1, 3.2, 3.3, 3.5, 6.4, 6.6, 7.7
Pearson Algebra 1 Common Core	4-1, 9-1, 9-3, 9-8
Reveal Algebra 1	3-4, 3-5, 3-6, 7-1, 11-1, 11-3, 11-7
SpringBoard Algebra 1	6, 29, 31, 35

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