What is the axis of symmetry (line that cuts/folds graph in half) of the graph? and what is the absolute maximum?

x - axis; there is no absolute max

Which two parent functions are not symmetric(cannot be cut in half) along the y axis?

f ( x ) = x f\left(x\right)=x f ( x ) = x

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">

graph the functions and check the graphs. Use desmos.com

f ( x ) = ∣ x ∣ f\left(x\right)=\left|x\right| f ( x ) = ∣ x ∣

f ( x ) = ∣ x ∣ f\left(x\right)=\left|x\right| f ( x ) = ∣ x ∣ is vertically compressed, reflected vertically, and translated six units down. Which of the following functions represents the transformation?

g ( x ) = − 1 2 ∣ x ∣ − 6 g\left(x\right)=-\frac{1}{2}\left|x\right|-6 g ( x ) = − 2 1 ∣ x ∣ − 6

g ( x ) = − 1 2 ∣ x − 6 ∣ g\left(x\right)=-\frac{1}{2}\left|x-6\right| g ( x ) = − 2 1 ∣ x − 6 ∣

g ( x ) = − 2 ∣ x ∣ − 6 g\left(x\right)=-2\left|x\right|-6 g ( x ) = − 2 ∣ x ∣ − 6

g ( x ) = − 2 ∣ x + 6 ∣ g\left(x\right)=-2\left|x+6\right| g ( x ) = − 2 ∣ x + 6 ∣

Describe the transformation given by − g ( x + 9 ) − 2 -g\left(x+9\right)-2 − g ( x + 9 ) − 2

Vertical reflection, shifted 9 units left, and shifted 2 units down.

Reflection over the x-axis, shifted 9 units right, and shifted 2 units down.

Reflection over the y-axis, shifted 9 units left, and shifted 2 units down.

Reflection over the x-axis, shifted 9 units left, and shifted 2 units up.

Which of the following notations describes the transformation needed to transform the red graph to the blue graph?

− 5 g ( x − 4 ) + 1 -5g\left(x-4\right)+1 − 5 g ( x − 4 ) + 1

5 g ( x − 4 ) + 1 5g\left(x-4\right)+1 5 g ( x − 4 ) + 1

− 1 5 g ( x − 4 ) + 1 -\frac{1}{5}g\left(x-4\right)+1 − 5 1 g ( x − 4 ) + 1

− 5 g ( x + 4 ) + 1 -5g\left(x+4\right)+1 − 5 g ( x + 4 ) + 1

Find the solution(s) to ∣ 2 x − 1 ∣ + 8 = 2 \left|2x-1\right|+8\ =2 ∣ 2 x − 1 ∣ + 8 = 2

Remember that the absolute value of a negative number is positive. The absolute value of a positive number stays positive.

Find the solution(s) to ∣ x − 7 ∣ − 2 = 4 \left|x-7\right|-2=4 ∣ x − 7 ∣ − 2 = 4

Remember that the absolute value of a negative number is positive. The absolute value of a positive number stays positive.

Solve for the solution(s) x if ∣ x − 15 ∣ − 5 < 16 |x-15|-5<16 ∣ x − 1 5 ∣ − 5 < 1 6

Hint: Simply, plug in a number that is in the set and check to see if it makes the inequalitiy true. Be sure to check all three sections.

What is the range of the following graph?

any real number greater than zero

Identify the domain and range.

Domain: between -3 and 4 Range: between 0 and 5

Is this a function? Why or why not?

Yes, because none of the domain numbers repeated.

Yes, because none of the range letters repeated.

No, because 3 goes to A and 4 goes to A.

Is this a function? Why or why not?

Yes, it passes the Vertical Line Test.

No, the domain numbers are repeated.

No, it passes the Vertical Line Test.

Yes, the range numbers are not repeated.

Is the relation a function? Why.

No, because the x-value 11 has two y-values pair with it.

Yes, because the x-value 11 has two y-values pair with it.

Yes, because each x-value has only one y-value paired with it.

No, because each x-value has only one y-value paired with it.

Domain and Range

Authored by Victoria Colbert

Mathematics

9th - 12th Grade

CCSS covered

Used 1+ times

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54 questions

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MULTIPLE CHOICE QUESTION

3 mins • 1 pt

What is the DOMAIN?

One way to think about the Domain is how far the graph extends left and to right along the x-axis. "How far does the graph reach to the left and right along the x-axis number line?"

(-4, ∞)

[-3, 3)

(-3, 3]

Tags

CCSS.8.F.A.1

CCSS.HSF.IF.B.5

MULTIPLE CHOICE QUESTION

3 mins • 1 pt

What is the RANGE?

{-3, 3]

all real numbers

[-4, 5]

One way to think about the Range is how far the graph extends down and up along the y-axis. "How far does the graph reach down and up along the y-axis number line?"

Tags

CCSS.8.F.A.1

CCSS.HSF.IF.B.5

MULTIPLE CHOICE QUESTION

3 mins • 1 pt

What is the RANGE?

(-∞, 0)

(0, ∞)

All real numbers

One way to think about the Range is how far the graph extends down and up along the y-axis. "How far does the graph reach down and up along the y-axis number line?"

Tags

CCSS.8.F.A.1

CCSS.HSF.IF.B.5

MULTIPLE CHOICE QUESTION

3 mins • 1 pt

What is the DOMAIN?

[0, ∞)

(-∞, 0)

All real numbers

One way to think about the Domain is how far the graph extends left to right along the x-axis. "How far does the graph reach to the left and right along the x-axis number line?"

Tags

CCSS.8.F.A.1

CCSS.HSF.IF.B.5

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the Range?

y ≥ 6

y ≤ 6

-10 ≤ y ≤ 6

One way to think about the Range is how far the graph extends down and up along the y-axis. "How far does the graph reach down and up along the y-axis number line?"

Tags

CCSS.HSF-IF.C.7A

MULTIPLE CHOICE QUESTION

1 min • 1 pt

What is the DOMAIN of this graph?

-7<x<5

-7≤x<5

-3<y<1

One way to think about the Domain is how far the graph extends left to right along the x-axis. "How far does the graph reach to the left and right along the x-axis number line?"

Tags

CCSS.8.F.A.1

CCSS.HSF.IF.B.5

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the Domain of the graph?

{xI -5 < x ≤ 1}

{xI -5 < x < 1}

{xI -5 ≤ x ≤ 1}

One way to think about the Domain is how far the graph extends left to right along the x-axis. "How far does the graph reach to the left and right along the x-axis number line?"

Tags

CCSS.8.F.A.1

CCSS.HSF.IF.B.5

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Domain and Range

What is the DOMAIN?

What is the RANGE?

What is the RANGE?

What is the DOMAIN?

What is the Range?

What is the DOMAIN of this graph?

What is the Domain of the graph?

What is the range of the graph?

What is the domain of the graph?

What is the range of the graph?

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