f ( x ) = x + 4 + 2 f\left(x\right)=\sqrt{x+4}+2 f ( x ) = x + 4 <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"> + 2 Describe the domain and range for the given function

Domain [ − 4 , ∞ ) \left[-4,\infty\right) [ − 4 , ∞ ) Range [ 2 , ∞ ) \left[2,\ \infty\right) [ 2 , ∞ )

Domain ( 4 , ∞ ) \left(4,\ \infty\right) ( 4 , ∞ ) Range ( − ∞ , ∞ ) \left(-\infty,\infty\right) ( − ∞ , ∞ )

Domain ( − 4 , ∞ ) \left(-4,\infty\right) ( − 4 , ∞ ) Range ( − ∞ , 2 ] \left(-\infty,\ 2\right] ( − ∞ , 2 ]

Domain [ 2 , ∞ ) \left[2,\ \infty\right) [ 2 , ∞ ) Range [ − 4 , ∞ ) \left[-4,\ \infty\right) [ − 4 , ∞ )

f ( x ) = 2 x + 4 f\left(x\right)=2x\ +4 f ( x ) = 2 x + 4 Describe the intercepts for the given function

x intercept (-2, 0) y-intercept (0, 4)

x intercept (0 , -2) y-intercept (4, 0)

x intercept (0, 4) y intercept (0, -2)

x intercept (4, 0) y intercept (-2, 0)

Describe the end behavior for the given graph

A s x a p p r o a c h e s − 4 , f ( x ) a p p r o a c h e s 1 As\ x\ approaches\ -4,\ f\left(x\right)\ approaches\ 1 A s x a p p r o a c h e s − 4 , f ( x ) a p p r o a c h e s 1 A s x a p p r o a c h e s 3 , f ( x ) a p p r o a c h e s − 1 As\ x\ approaches\ 3,\ f\left(x\right)\ approaches\ -1 A s x a p p r o a c h e s 3 , f ( x ) a p p r o a c h e s − 1

( − 4 , 3 ) \left(-4,\ 3\right) ( − 4 , 3 )

A s x a p p r o a c h e s 1 , f ( x ) a p p r o a c h e s − 4 As\ x\ approaches\ 1,\ f\left(x\right)\ approaches\ -4 A s x a p p r o a c h e s 1 , f ( x ) a p p r o a c h e s − 4 A s x a p p r o a c h e s − 1 , f ( x ) a p p r o a c h e s 3 As\ x\ approaches\ -1,\ f\left(x\right)\ approaches\ 3 A s x a p p r o a c h e s − 1 , f ( x ) a p p r o a c h e s 3

Which statement is invalid from the given graph

The increasing interval is ( − 1 , 1 ) \left(-1,\ 1\right) ( − 1 , 1 )

T h e A b s o l u t e M a x i m u m i s 3 w h e n x = − 2 The\ Absolute\ Maximum\ is\ 3\ when\ x\ =\ -2 T h e A b s o l u t e M a x i m u m i s 3 w h e n x = − 2

T h e L o c a l M i n i m u m i s a t − 1 w h e n x = 0 The\ Local\ Minimum\ is\ at\ -1\ when\ x\ =0 T h e L o c a l M i n i m u m i s a t − 1 w h e n x = 0

T h e R a n g e i s [ − 1 , 3 ] The\ Range\ is\ \left[-1,\ 3\right] T h e R a n g e i s [ − 1 , 3 ]

Find the function that is finally graphed after the following transformations are applied to the graph of y = ∣ x ∣ y\ =\ \left|x\right| y = ∣ x ∣ The graph is shifted right 3 units, stretched by a factor of 3, shifted vertically down 2 units, and finally reflected across the x-axis.

y = − ( 3 ∣ x − 3 ∣ − 2 ) y=-\left(3\left|x-3\right|-2\right) y = − ( 3 ∣ x − 3 ∣ − 2 )

y = − 3 ∣ x − 3 ∣ − 2 y=-3\left|x-3\right|-2 y = − 3 ∣ x − 3 ∣ − 2

y = − ( 3 ∣ x + 3 ∣ − 2 ) y=-\left(3\left|x+3\right|-2\right) y = − ( 3 ∣ x + 3 ∣ − 2 )

y = 3 ∣ − x − 3 ∣ − 2 y=3\left|-x-3\right|-2 y = 3 ∣ − x − 3 ∣ − 2

Match the graph to the correct functions

f ( x ) = x − 1 f\left(x\right)=\sqrt{x-1} f ( x ) = x − 1 <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">

f ( x ) = x f\left(x\right)=\sqrt{x} f ( x ) = x <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">

f ( x ) = x + 1 f\left(x\right)=\sqrt{x+1} f ( x ) = x + 1 <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">

f ( x ) = x − 1 f\left(x\right)=x-1 f ( x ) = x − 1

Describe the Absolute Maximum and Absolute Minimum for the given graph

Absolute Max is 6 , when x = 5 Absolute Min is 1, when x =2

Absolute Max is 2, when x = 7 Absolute Min is 3, when x = 0

Absolute Max is 5, when x = 6 Absolute Min is 2, when x =1

Absolute Max is 7, when x = 2 Absolute Min is 0, when x =3

Unit 1 Parent Functions and Their Key Features Unit Test

Authored by Genevieve MillbrookHS

Mathematics

11th - 12th Grade

CCSS covered

Used 56+ times

Unit 1 Parent Functions and Their Key Features Unit Test

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18 questions

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MULTIPLE CHOICE QUESTION

2 mins • 1 pt

The range for a quadratic function is all real numbers.

True

False; the domain of a quadratic function is all real numbers

False; the range of a quadratic function is undefined

Tags

CCSS.HSF-IF.C.7A

MULTIPLE CHOICE QUESTION

2 mins • 1 pt

The quadratic function
$f\left(x\right)\ =\ x^2\ -\ 2\ has\ a\ domain\ of\ \left[-2,\ \infty\right)$

True

False; the domain is $\left[2,\ \infty\right)$

False; the domain is $\left(2,\ \infty\right)$

False; the domain is all real numbers

Tags

CCSS.HSA.REI.D.10

CCSS.HSA.REI.D.11

CCSS.HSA.SSE.A.1

MULTIPLE CHOICE QUESTION

2 mins • 1 pt

If you have a translated function in the form
$f\left(x\right)\ =\ \left(x-h\right)^2\ -\ k\ ,\$ the graph shifted h units right, and k units down.

True

False; the graph shifted h units left, and k units down

False; the graph shifted h units right, and k units up

False; the graph shifted h units left, and k unit up

Tags

CCSS.HSF.BF.B.3

CCSS.HSF.IF.C.7

MULTIPLE CHOICE QUESTION

2 mins • 1 pt

If
$f\left(x\right)\ =\ \sqrt{x}$ has a reflection about the x-axis, its new function is $f\left(x\right)\ =\ -\sqrt{x}$

True

False; The reflection is about the y-axis

False; The reflection about the x-axis will yield a new function $f\left(x\right)=\sqrt{-x}$

Tags

CCSS.HSF.BF.B.3

MULTIPLE CHOICE QUESTION

2 mins • 1 pt

$f\left(x\right)\ =\ 5^x$
The function given has a y-intercept of (0, 5)

True

False; The y intercept is undefined

False; The y-intercept is (0, 1)

Tags

CCSS.HSF-IF.C.7E

MULTIPLE CHOICE QUESTION

2 mins • 1 pt

If a function crosses an axis at (a, 0), this location is known as an x-intercept of the function.

True

False; The x-intercept is (0, a)

False; The y-intercept is (a, 0)

Tags

CCSS.HSA.REI.D.11

CCSS.HSA.APR.B.2

CCSS.HSA.APR.B.3

CCSS.HSA.REI.B.4

CCSS.HSA.REI.C.7

MULTIPLE CHOICE QUESTION

2 mins • 1 pt

$f\left(x\right)=\sqrt{x+4}+2$
Describe the domain and range for the given function

Domain $\left(4,\ \infty\right)$ Range $\left(-\infty,\infty\right)$

Domain $\left[-4,\infty\right)$ Range $\left[2,\ \infty\right)$

Domain $\left(-4,\infty\right)$ Range $\left(-\infty,\ 2\right]$

Domain $\left[2,\ \infty\right)$ Range $\left[-4,\ \infty\right)$

Tags

CCSS.HSF.IF.A.1

CCSS.HSF.IF.A.2

CCSS.HSF.IF.B.5

MULTIPLE CHOICE QUESTION

2 mins • 1 pt

$f\left(x\right)=4-x^2$
Describe the positive interval the given function

$\left(-\infty,0\right)$

$\left(-2,\ 2\right)$

$\left(-\infty,\ -2\right)\cup\ \left(2,\ \infty\right)$

$\left(0,\ \infty\right)$

Tags

CCSS.HSF-IF.C.7A

MULTIPLE CHOICE QUESTION

2 mins • 1 pt

$f\left(x\right)=4\ -\ x^2$
Describe the negative interval for the given function

$\left(-\infty,0\right)$

$\left(-2,\ 2\right)$

$\left(-\infty,\ -2\right)\cup\ \left(2,\infty\right)$

$\left(0,\ \infty\right)$

Tags

CCSS.HSF-IF.C.7E

10.

MULTIPLE CHOICE QUESTION

2 mins • 1 pt

$f\left(x\right)\ =4\ -x^2$
Describe the increasing interval for the given function

$\left(-\infty,\ 0\right)$

$\left(-2,2\right)$

$\left(-\infty,\ -2\right)\cup\ \left(2,\ \infty\right)$

$\left(0,\ \infty\right)$

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Unit 1 Parent Functions and Their Key Features Unit Test

The range for a quadratic function is all real numbers.

The quadratic function f(x) = x2 − 2 has a domain of [−2, ∞)f\left(x\right)\ =\ x^2\ -\ 2\ has\ a\ domain\ of\ \left[-2,\ \infty\right)f(x) = x2 − 2 has a domain of [−2, ∞)

If you have a translated function in the form f(x) = (x−h)2 − k , f\left(x\right)\ =\ \left(x-h\right)^2\ -\ k\ ,\ f(x) = (x−h)2 − k , the graph shifted h units right, and k units down.

If f(x) = xf\left(x\right)\ =\ \sqrt{x}f(x) = x​ has a reflection about the x-axis, its new function is f(x) = −xf\left(x\right)\ =\ -\sqrt{x}f(x) = −x​

f(x) = 5xf\left(x\right)\ =\ 5^xf(x) = 5x The function given has a y-intercept of (0, 5)

If a function crosses an axis at (a, 0), this location is known as an x-intercept of the function.

f(x)=x+4+2f\left(x\right)=\sqrt{x+4}+2f(x)=x+4​+2 Describe the domain and range for the given function

f(x)=4−x2f\left(x\right)=4-x^2f(x)=4−x2 Describe the positive interval the given function

f(x)=4 − x2f\left(x\right)=4\ -\ x^2f(x)=4 − x2 Describe the negative interval for the given function

f(x) =4 −x2f\left(x\right)\ =4\ -x^2f(x) =4 −x2 Describe the increasing interval for the given function

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The quadratic function
$f\left(x\right)\ =\ x^2\ -\ 2\ has\ a\ domain\ of\ \left[-2,\ \infty\right)$

If you have a translated function in the form
$f\left(x\right)\ =\ \left(x-h\right)^2\ -\ k\ ,\$ the graph shifted h units right, and k units down.

If
$f\left(x\right)\ =\ \sqrt{x}$ has a reflection about the x-axis, its new function is $f\left(x\right)\ =\ -\sqrt{x}$

$f\left(x\right)\ =\ 5^x$
The function given has a y-intercept of (0, 5)

$f\left(x\right)=\sqrt{x+4}+2$
Describe the domain and range for the given function

$f\left(x\right)=4-x^2$
Describe the positive interval the given function

$f\left(x\right)=4\ -\ x^2$
Describe the negative interval for the given function

$f\left(x\right)\ =4\ -x^2$
Describe the increasing interval for the given function