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Aloiza [94]
3 years ago
13

Translate ƒ(x) = |x| so that it's translated up by 5 units and vertically stretched by a factor of 3. What's the new function g(

x)? Question 20 options: A) g(x) = |3x| + 5 B) g(x) = |3x| +–5 C) g(x) = 3|x| +–5 D) g(x) = 3|x| + 5
Mathematics
1 answer:
zavuch27 [327]3 years ago
5 0

Given:

The parent absolute function is

f(x)=|x|

To find:

The new function if the parent function is translated up by 5 units and vertically stretched by a factor of 3.

Solution:

The translation is defined as

g(x)=kf(x+a)+b                .... (1)

Where, k is stretch factor, a is horizontal shift and b is vertical shift.

If 0<k<1, then the graph compressed vertically by factor k and if k>1, then the graph stretch vertically by factor k.

If a>0, then the graph shifts a units left and if a<0, then the graph shifts a units right.

If b>0, then the graph shifts b units up and if b<0, then the graph shifts b units down.

Parent function is translated up by 5 units. So, b=5

It is vertically stretched by a factor of 3. So, k=3.

There is no horizontal shift. So, a=0.

Now, putting k=3, a=0 and b=5 in (1), we get

g(x)=3f(x+0)+5

g(x)=3f(x)+5

g(x)=3|x|+5       [\because f(x)=|x|]

Therefore, the correct option is D.

You might be interested in
50 BIG POINTS! Help me on math please!  @ Apologiabiology, @ Bookishfairy73
nekit [7.7K]
Rate of change is also knkown as slope which is found by
\frac{y2-y1}{x2-x1}=slope if you know 2 points/ordered pairs
aos, if x incheases while y decreases then slope is negative
when x increases while y increases then slpe if positive
also, if you can convert to y=mx+b, m=slope
another thing if you have ax+by=c then slope=-a/b

so first one
2x-5y=15
a=2
b=-5
-2/-5=2/5
slope=2/5
positive

next
y=-4x
-4 =slope=negative


x increases while y decreases
negative

x increases while y decreases
negative


so
Positive
Negative
Negative
Negative





A. 6x-3y=12
sloope=-6/-3=2

B. y=5x+b
slope=5

C. (8-2)/(3-1)=6/2=3
sloope=3

D. goes up 4 units and goes right 1 unit, 4/1=4
sloope=4


5 is greates
B is the answer









A. (6-3)/(4-3)=3/1=3
slope=3

B. y=4+6x
slope=6


C.12x+6y=18
slope=-12/6=-2

D. goes down 5 units as it goest 1 uniit to right aka -5./1
slope=-5


greatest is 6
B is answer











the starting value I would guess si when x=1 what is the greats y value

look at each
first one
A. x=1 and =-3

B.y=3x-8
y=3(1)-8
y=3-8
y=-5

C. 8x+4y=16
8(1)+4y=16
8+4y=16
4y=8
y=2

D. at 1 unit to right it is 1 nit up so y=1


greatest is  2 or C





so just subsitute 1 for x since x represents how many teaspoons
y=16(1)560
y=16+560
y=576 caloris for 1 sugar teaspoon

for honey, just read off the graph
for when x=1
y=504

so calores of sugar=576
calories in honey=504






ANSWERS

Postive
Negative
Negative
Negative

B

B

C

sugar=576
honey=504
4 0
2 years ago
Read 2 more answers
Hi! Please help, I'd appreciate it!
Romashka-Z-Leto [24]

The volume of sphere is \frac{1372}{3}\pi feet cubed.

Step-by-step explanation:

Given,

Surface area of sphere = 196π square feet

Surface area of sphere = 4πr²

We will find radius of sphere.

4\pi r^2=196\pi

Dividing both sides by 4π

\frac{4\pi r^2}{4\pi}=\frac{196\pi}{4\pi}\\\\r^2=49

Taking square root on both sides

\sqrt{r^2}=\sqrt{49}\\r=7

The radius is 7 feet.

Volume of sphere = \frac{4}{3}\pi r^3

Volume=\frac{4}{3}\pi (7)^3\\\\Volume= \frac{4}{3}\pi *343\\\\Volume = \frac{1372}{3}\pi

The volume of sphere is \frac{1372}{3}\pi feet cubed.

Keywords: volume, surface area

Learn more about surface area at:

  • brainly.com/question/101683
  • brainly.com/question/103144

#LearnwithBrainly

3 0
2 years ago
Given f(x)=3x-1 find f(-1)
vaieri [72.5K]

Answer:

<h2>f( - 1) = - 4</h2>

Step-by-step explanation:

f(x) = 3x - 1

To find f(-1) substitute the value of x that's

- 1 into f(x). That's for every x in f(x) replace it with - 1 and solve

That's

f( - 1) = 3(-1) - 1

= - 3 - 1

We have the final answer as

<h3>f(-1) = - 4</h3>

Hope this helps you

7 0
3 years ago
For which equation would x = 0 be a solution?
Vesna [10]

Answer:

x/9.074

Step-by-step explanation:

this is the equation that gives the correct answer

0/9.074=0

6 0
3 years ago
Which of the following are incorrect expressions for slope?
vfiekz [6]

Answer:

Option B and C are correct.

\frac{x_2-x_1}{y_2-y_1}

\frac{run}{rise} are the expression incorrect for slope

Step-by-step explanation:

Slope is defined as the change in the dependent variable  relative to the change in the dependent variable

or the ratio of the horizontal changes to vertical changes between any two points on the graph of the line.

The vertical changes between any two points is rise

The horizontal changes between any two points is run.

Formula for slope is given by:

For any two points (x_1, y_1) and (x_2, y_2)

then slope is:

\text{Slope} =\frac{rise}{run}= \frac{y_2-y_1}{x_2-x_1}

or we can write this as:

Δy = y_2-y_1

Δx = x_2-x_1

⇒\text{Slope} = \frac{\triangle y}{\triangle x}

Therefore, the expression which are incorrect for slope  are;

\frac{x_2-x_1}{y_2-y_1}

\frac{run}{rise}

8 0
2 years ago
Read 2 more answers
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