2 \sqrt{2} 2 <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z">

state the minimum value and the number where this min occurs:

min value is -4, occurring when x = 1

min value is 1, occurring when x = 4

min value is 1, occurring when x = -4

min value is 4, occurring when x = 1

Which equation represents point-slope form?

y − y 1 = m ( x − x 1 ) y\ -\ y_1\ =\ m\left(x\ -\ x_1\right) y − y 1 = m ( x − x 1 )

y = m x + b y\ =\ mx+b y = m x + b

A x + B y + C = 0 Ax\ +\ By\ +\ C\ =\ 0 A x + B y + C = 0

m = y 2 − y 1 x 2 − x 1 m=\frac{y_2-y_1}{x_2-x_1} m = x 2 − x 1 y 2 − y 1

Which equation represents slope-intercept form?

y = m x + b y\ =\ mx\ +\ b y = m x + b

y − y 1 = m ( x − x 1 ) y\ -\ y_1\ =\ m\left(x\ -\ x_1\right) y − y 1 = m ( x − x 1 )

A x + B y + C = 0 Ax\ +\ By\ +\ C\ =\ 0 A x + B y + C = 0

m = y 2 − y 1 x 2 − x 1 m=\frac{y_2-y_1}{x_2-x_1} m = x 2 − x 1 y 2 − y 1

Which equation represents General Form?

A x + B y + C = 0 Ax+By+C=0 A x + B y + C = 0

y − y 1 = m ( x − x 1 ) y-y_1=m\left(x-x_1\right) y − y 1 = m ( x − x 1 )

All vertical lines have the form of:

m = y 2 − y 1 x 2 − x 1 m=\frac{y_2-y_1}{x_2-x_1} m = x 2 − x 1 y 2 − y 1

Write the equation in point-slope form for the line that contains the points (3, -5) and (5, -1)

y + 1 = 2 ( x − 5 ) y+1=2\left(x-5\right) y + 1 = 2 ( x − 5 )

y − 5 = − 1 ( x + 1 ) y-5=-1\left(x+1\right) y − 5 = − 1 ( x + 1 )

y + 1 = 1 2 ( x − 5 ) y+1=\frac{1}{2}\left(x-5\right) y + 1 = 2 1 ( x − 5 )

y − 5 = 1 2 ( x + 1 ) y-5=\frac{1}{2}\left(x+1\right) y − 5 = 2 1 ( x + 1 )

Convert y + 2 = − 3 ( x − 5 ) y+2=-3\left(x-5\right) y + 2 = − 3 ( x − 5 ) into slope-intercept form:

y = − 3 x + 13 y=-3x+13 y = − 3 x + 1 3

y = − 3 x + 3 y=-3x+3 y = − 3 x + 3

y = − 3 x − 7 y=-3x-7 y = − 3 x − 7

y = − 3 x − 17 y=-3x-17 y = − 3 x − 1 7

What is the average rate of change between x 1 =16 and x 2 =18

f ( 18 ) − f ( 16 ) 18 − 16 = 530 − 430 18 − 16 = 50 \frac{f\left(18\right)-f\left(16\right)}{18-16}=\ \frac{530-430}{18-16}=50 1 8 − 1 6 f ( 1 8 ) − f ( 1 6 ) = 1 8 − 1 6 5 3 0 − 4 3 0 = 5 0

f ( 18 ) − f ( 16 ) 18 − 16 = 590 − 430 18 − 16 = 80 \frac{f\left(18\right)-f\left(16\right)}{18-16}=\frac{590-430}{18-16}=80 1 8 − 1 6 f ( 1 8 ) − f ( 1 6 ) = 1 8 − 1 6 5 9 0 − 4 3 0 = 8 0

f ( 18 ) − f ( 16 ) 18 − 16 = 18 − 16 18 − 16 = 1 \frac{f\left(18\right)-f\left(16\right)}{18-16}=\frac{18-16}{18-16}=\ 1 1 8 − 1 6 f ( 1 8 ) − f ( 1 6 ) = 1 8 − 1 6 1 8 − 1 6 = 1

Functions and their Graphs

Authored by Lynne Fearer

Mathematics

10th - 12th Grade

CCSS covered

Used 177+ times

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MULTIPLE CHOICE QUESTION

5 mins • 1 pt

f(-1) =

-4

-2

$\sqrt{2}$

Tags

CCSS.HSF.IF.A.2

MULTIPLE CHOICE QUESTION

5 mins • 1 pt

f(1) =

-1

Tags

CCSS.HSF.IF.A.2

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

domain interval of f

(- $\infty$ , $\infty$ )

[0, $\infty$ )

[-2, 4]

[0, 3]

Tags

CCSS.8.F.A.1

CCSS.HSF.IF.B.5

MULTIPLE CHOICE QUESTION

5 mins • 1 pt

range interval of f

( - $\infty$ , $\infty$ )

[0, $\infty$ )

[-2, 4]

[0, 5]

Tags

CCSS.8.F.A.1

CCSS.HSF.IF.B.5

MULTIPLE CHOICE QUESTION

5 mins • 1 pt

decreasing interval of f

( - $\infty$ , 1)

( - $\infty$ , 1]

( - $\infty$ , 0]

( - $\infty$ , $\infty$ )

Tags

CCSS.HSA.REI.D.10

MULTIPLE CHOICE QUESTION

5 mins • 1 pt

increasing interval of f

( 2 , $\infty$ )

[0, 1] $\cup$ (2, $\infty$ )

[0, 1] $\cup$ [2, $\infty$ )

[0, $\infty$ )

Tags

CCSS.HSA.REI.D.10

MULTIPLE CHOICE QUESTION

5 mins • 1 pt

constant interval of f

(1, 2)

[1, 2)

[1, 2]

(1, 2]

Tags

CCSS.HSF-IF.C.7B

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Functions and their Graphs

f(-1) =

f(1) =

domain interval of f

range interval of f

decreasing interval of f

increasing interval of f

constant interval of f

the value(s) of x for which f(x) = 1

state the minimum value and the number where this min occurs:

name the x-intercept(s)

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