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(Get the variable on a side by itself)
there are addition or subtraction signs, add oppos ite to both sides of equation to get the variable erm by itself.

x+6=9

x-3=8

4+x=-8
dd (-6)

-5=x+8

3+t=21

-9.7=-4.7+y
there is a coefficient (number) on the variable, divide both sides of the equation by that coefficiel number) to get the variable by itself.

2x_=6_

3x=-9

-4x=-16

.8x=.16
livide by 22

x=3

-20=-5w

18=-9m

-4x=.8

-x=-18

-t=40

-15=-w

-f=5

11=-2m

Mixed Practice. Solve these equations by using the two steps:

If there are addition or subtraction signs, add oppos te to both sides of

(Get the variable on a side by itself) $\newline$ there are addition or subtraction signs, add oppos ite to both sides of equation to get the variable erm by itself. $\newline$ $1$ . $x+6=9$ $\newline$ $2$ . $x-3=8$ $\newline$ $3$ . $4+x=-8$ $\newline$ dd ( $-6$ ) $\newline$ $4$ . $-5=x+8$ $\newline$ $5$ . $3+t=21$ $\newline$ $6$ . $-9.7=-4.7+y$ $\newline$ there is a coefficient (number) on the variable, divide both sides of the equation by that coefficiel number) to get the variable by itself. $\newline$ $1$ . $\underline{2 x}=\underline{6}$ $\newline$ $2$ . $3 x=-9$ $\newline$ $3$ . $-4 \mathrm{x}=-16$ $\newline$ $4$ . $.8 \mathrm{x}=.16$ $\newline$ livide by $22$ $\newline$ $\mathrm{x}=3$ $\newline$ $5$ . $x-3=8$ $0$ $\newline$ $6$ . $x-3=8$ $1$ $\newline$ $7$ . $x-3=8$ $2$ $\newline$ $7$ . $x-3=8$ $3$ $\newline$ $8$ . $x-3=8$ $4$ $\newline$ $9$ . $x-3=8$ $5$ $\newline$ $10$ . $x-3=8$ $6$ $\newline$ $11$ . $x-3=8$ $7$ $\newline$ Mixed Practice. Solve these equations by using the two steps: $\newline$ $1$ . If there are addition or subtraction signs, add oppos te to both sides of

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Transformations of functions

Full solution

Q. (Get the variable on a side by itself)

\newline

there are addition or subtraction signs, add oppos ite to both sides of equation to get the variable erm by itself.

\newline

1

.

x+6=9

\newline

2

.

x-3=8

\newline

3

.

4+x=-8

\newline

dd (

-6

)

\newline

4

.

-5=x+8

\newline

5

.

3+t=21

\newline

6

.

-9.7=-4.7+y

\newline

there is a coefficient (number) on the variable, divide both sides of the equation by that coefficiel number) to get the variable by itself.

\newline

1

.

\underline{2 x}=\underline{6}

\newline

2

.

3 x=-9

\newline

3

.

-4 \mathrm{x}=-16

\newline

4

.

.8 \mathrm{x}=.16

\newline

livide by

22

\newline

\mathrm{x}=3

\newline

5

.

x-3=8

0

\newline

6

.

x-3=8

1

\newline

7

.

x-3=8

2

\newline

7

.

x-3=8

3

\newline

8

.

x-3=8

4

\newline

9

.

x-3=8

5

\newline

10

.

x-3=8

6

\newline

11

.

x-3=8

7

\newline

Mixed Practice. Solve these equations by using the two steps:

\newline

1

. If there are addition or subtraction signs, add oppos te to both sides of

Subtract to isolate x: Solve $x + 6 = 9$ by subtracting $6$ from both sides to isolate $x$ . Calculation: $x + 6 - 6 = 9 - 6$ , which simplifies to $x = 3$ .
Add to isolate x: Solve $x - 3 = 8$ by adding $3$ to both sides to isolate $x$ . Calculation: $x - 3 + 3 = 8 + 3$ , which simplifies to $x = 11$ .
Subtract to isolate x: Solve $4 + x = -8$ by subtracting $4$ from both sides to isolate $x$ . Calculation: $4 + x - 4 = -8 - 4$ , which simplifies to $x = -12$ .
Subtract to isolate x: Solve $-5 = x + 8$ by subtracting $8$ from both sides to isolate $x$ . Calculation: $-5 - 8 = x + 8 - 8$ , which simplifies to $x = -13$ .
Subtract to isolate $t$ : Solve $3 + t = 21$ by subtracting $3$ from both sides to isolate $t$ . Calculation: $3 + t - 3 = 21 - 3$ , which simplifies to $t = 18$ .
Subtract to isolate $y$ : Solve $-9.7 = -4.7 + y$ by subtracting $-4.7$ from both sides to isolate $y$ . Calculation: $-9.7 - (-4.7) = -4.7 + y - (-4.7)$ , which simplifies to $y = -5$ .
Divide to isolate x: Solve $2x = 6$ by dividing both sides by $2$ to isolate $x$ . Calculation: $\frac{2x}{2} = \frac{6}{2}$ , which simplifies to $x = 3$ .
Divide to isolate $x$ : Solve $3x = -9$ by dividing both sides by $3$ to isolate $x$ . Calculation: $\frac{3x}{3} = \frac{-9}{3}$ , which simplifies to $x = -3$ .
Divide to isolate $x$ : Solve $-4x = -16$ by dividing both sides by $-4$ to isolate $x$ . Calculation: $-4x / -4 = -16 / -4$ , which simplifies to $x = 4$ .
Divide to isolate x: Solve $0.8x = 0.16$ by dividing both sides by $0.8$ to isolate $x$ . Calculation: $0.8x / 0.8 = 0.16 / 0.8$ , which simplifies to $x = 0.2$ .
Divide to isolate $w$ : Solve $-20 = -5w$ by dividing both sides by $-5$ to isolate $w$ . Calculation: $-20 / -5 = -5w / -5$ , which simplifies to $w = 4$ .
Divide to isolate $m$ : Solve $18 = -9m$ by dividing both sides by $-9$ to isolate $m$ . Calculation: $\frac{18}{-9} = \frac{-9m}{-9}$ , which simplifies to $m = -2$ .
Divide to isolate $x$ : Solve $-4x = 0.8$ by dividing both sides by $-4$ to isolate $x$ . Calculation: $-4x / -4 = 0.8 / -4$ , which simplifies to $x = -0.2$ .
Divide to isolate $x$ : Solve $-x = -18$ by dividing both sides by $-1$ to isolate $x$ . Calculation: $-x / -1 = -18 / -1$ , which simplifies to $x = 18$ .
Divide to isolate $t$ : Solve $-t = 40$ by dividing both sides by $-1$ to isolate $t$ . Calculation: $-t / -1 = 40 / -1$ , which simplifies to $t = -40$ .
Divide to isolate $w$ : Solve $-15 = -w$ by dividing both sides by $-1$ to isolate $w$ . Calculation: $-15 / -1 = -w / -1$ , which simplifies to $w = 15$ .
Divide to isolate $f$ : Solve $-f = 5$ by dividing both sides by $-1$ to isolate $f$ . Calculation: $-f / -1 = 5 / -1$ , which simplifies to $f = -5$ .
Divide to isolate $m$ : Solve $11 = -2m$ by dividing both sides by $-2$ to isolate $m$ . Calculation: $\frac{11}{-2} = \frac{-2m}{-2}$ , which simplifies to $m = -5.5$ .

More problems from Transformations of functions

Question

g(x)

g(x)

is the reflection across the x-axis of

f(x)=9|x+2|-4

\newline

\newline

\text{}(A)g(x) = 9|x+2| - 4\text{]}

\newline

\text{}(B)g(x) = 9|x-2| - 4\text{]}

\newline

\text{}(C)g(x)=-9|x-2| +4\text{]}

\newline

\text{(D)}g(x) = -9|x + 2| + 4\text{]}

Posted 2 months ago

Question

What does the transformation

f(x) \mapsto f(x - 4)

do to the graph of

f(x)

\newline

\newline

\text{translates it } 4 \text{ units right}

\newline

\text{translates it } 4 \text{ units down}

\newline

\text{translates it } 4 \text{ units left}

\newline

\text{translates it } 4 \text{ units up}

Posted 2 months ago

Question

What does the transformation

f(x) \mapsto f(4x)

do to the graph of

f(x)

\newline

\newline

[A] stretches it vertically

\newline

[B] stretches it horizontally

\newline

[C]shrinks it horizontally

\newline

[D]shrinks it vertically

Posted 1 month ago

Question

g(x)

g(x)

is the translation

9

f(x) = 10x + 8

\newline

\newline

g(x) = 10x - 82

\newline

g(x) = 10x + 98

\newline

g(x) = 10x - 1

\newline

g(x) = 10x + 17

Posted 2 months ago

Question

What kind of transformation converts the graph of

f(x) = -3x^2 - 4

into the graph of

g(x) = -3x^2 + 6

\newline

\newline

\text{[A]translation 10 units up}

\newline

\text{[B]translation 10 units down}

\newline

\text{[C]translation 10 units left}

\newline

\text{[D]translation 10 units right}

Posted 1 month ago

Question

y=x^{2}

is scaled vertically by a factor of

7

. What is the equation of the new parabola?

\newline

y=

Posted 4 months ago

Question

y=x^{2}

is shifted down by

6

units and to the right by

5

\newline

What is the equation of the new parabola?

\newline

y=

Posted 4 months ago

Question

y=x^{2}

is shifted up by

2

units and to the right by

3

\newline

What is the equation of the new parabola?

\newline

y=

Posted 1 month ago

Question

y=x^{2}

is reflected across the

x

-axis and then scaled vertically by a factor of

5

\newline

What is the equation of the new parabola?

\newline

y=\square

Posted 2 months ago

Question

y=x^{2}

is scaled vertically by a factor of

\frac{1}{10}

\newline

What is the equation of the new parabola?

\newline

y=

Posted 3 months ago