List the types of intervals that the graph demonstrates in order.

increasing, constant, decreasing, constant

decreasing, constant, increasing, constant

increasing, decreasing, constant

increasing, constant, increasing, constant

What are all the x-intercepts?

(−3,0), (−2,0), (2,0), (3,0)

The function shown in the graph is:

Odd because it's can be rotated 180 degrees about the origin

Even because it's reflected across the y-axis.

Odd because it's reflected across the y-axis.

Even because it's can be rotated 180 degrees about the origin

Is this function even, odd or neither?

Even because it can be reflected across the y-axis

Odd because it can be reflected across the y-axis

Even because it can be rotated 180 degrees about the origin

Odd because it can be rotated 180 degrees about the origin

Neither even nor odd, this is not a function.

Find f(0) in this piecewise function.

f(0) is undefined for this graph.

Evaluate f ( x ) f\left(x\right) f ( x ) for x = − 9 x=-9 x = − 9 and x = 5 x=5 x = 5

f ( − 9 ) = 15 , f ( 5 ) = 0 f\left(-9\right)=15,\ f\left(5\right)=0 f ( − 9 ) = 1 5 , f ( 5 ) = 0

f ( − 9 ) = 0 , f ( 5 ) = 15 f\left(-9\right)=0,\ f\left(5\right)=15 f ( − 9 ) = 0 , f ( 5 ) = 1 5

f ( − 9 ) = 0 , f ( 5 ) = − 6 f\left(-9\right)=0,\ f\left(5\right)=-6 f ( − 9 ) = 0 , f ( 5 ) = − 6

f ( − 9 ) = 15 , f ( 5 ) = − 6 f\left(-9\right)=15,\ f\left(5\right)=-6 f ( − 9 ) = 1 5 , f ( 5 ) = − 6

Which piecewise function corresponds to this graph? (Take your time)

f(x) = { -x+1 if x < 4; x if x ≥ 4

f(x) = { x if x < 4; -x+1 if x ≥ 4

f(x) = { x if x ≤ 4; -x+1 if x > 4

f(x) = { -x+1 if x ≤ 4; x if x > 4

What are the transformations to the graph compared to the parent function of y = x y=\sqrt{x} y = 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"> Check all that apply.

y = − x − 2 + 3 y=-\sqrt{x-2}+3 y = − x − 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"> + 3

reflection over x-axis: vertical shift up 3; horizontal shift right 2

reflection over y-axis: vertical shift up 3; horizontal shift right 2

y = − x + 2 + 3 y=-\sqrt{x+2}+3 y = − x + 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"> + 3

y = − x − 3 + 2 y=-\sqrt{x-3}+2 y = − x − 3 <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

What are the transformations for the graph of the parent function f(x) = √x to the function above

vertical stretch up 2; vertical shift down 5

vertical shift up 2; vertical shift down 5

vertical stretch up 2; vertical stretch down 5

vertical stretch up 2; horizontal shift down 5

Given the blue graph is the the parent function y = x y=\sqrt{x} y = 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"> Which equation will transform the blue parent function to the red graph?

y = − x y=-\sqrt{x} y = − 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">

y = − x y=\sqrt{-x} y = − 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">

y = x − 1 y=\sqrt{x}-1 y = 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"> − 1

y = x − 1 y=\sqrt{x-1} y = 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">

What transformation is represented by f ( − x ) f\left(-x\right) f ( − x ) ?

Rotation about the origin 180 degrees

Find f(3) in this piecewise function.

f(3) is undefined for this graph.

#3 PC Properties of Functions

Authored by Shayla Bushhousen

Mathematics

9th - 12th Grade

CCSS covered

Used 25+ times

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34 questions

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MULTIPLE CHOICE QUESTION

2 mins • 1 pt

What is the domain of the graph?

[-∞,∞]

(-∞,∞)

[-3, 3]

(-3, 3)

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the range of this function?
Please note the scale of the axis.

[-5, 5]

(1.5, 4)

[3, 8]

(-6, 6]

MULTIPLE CHOICE QUESTION

2 mins • 1 pt

What is the domain of the relation?
Please note the scale of the axis.

(-∞, ∞)

(-2, 2)

(-3, 3)

[-4, 5)

MULTIPLE CHOICE QUESTION

3 mins • 1 pt

What is the range of the function?
Please note the scale of the axis.

(-∞, 3]

(-∞, ∞)

[3, ∞)

(-6, 3]

MULTIPLE CHOICE QUESTION

1 min • 1 pt

Is the relation shown a function?

No, because not every input has a single output.

Yes, because every input does has a single output.

No, because every Y value is paired with an X value.

Yes, because every Y value is paired with an X value.

MULTIPLE CHOICE QUESTION

1 min • 1 pt

Is the relation shown in the mapping a function?

Yes, every Y value is paired with an X value.

Yes, because every input is paired with exactly one output.

No, not every Y value is pared once.

No, because not every input is paired with exactly one output.

MULTIPLE CHOICE QUESTION

3 mins • 1 pt

What are the local maxima of this graph?

local maximum at (2.2, 3.9)

local maximum at (-8, 5)

local maximum at (5, -8) & (3.9, 2.2)

local maximum at (-8, 5) & (2.2, 3.9)

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#3 PC Properties of Functions

What is the domain of the graph?

What is the range of this function?Please note the scale of the axis.

What is the domain of the relation?Please note the scale of the axis.

What is the range of the function?Please note the scale of the axis.

Is the relation shown a function?

Is the relation shown in the mapping a function?

What are the local maxima of this graph?

List the types of intervals that the graph demonstrates in order.

Approximately what interval(s) is the function decreasing?

What are all the x-intercepts?

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What is the range of this function?
Please note the scale of the axis.

What is the domain of the relation?
Please note the scale of the axis.

What is the range of the function?
Please note the scale of the axis.