1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Nonamiya [84]
3 years ago
14

The graph of the function f(x) = log5 (x) is stretched vertically by a factor of 2, shifted to the left by 8 units, and shifted

up
by 3 units.
Find the equation of the function g(x) described above.

Mathematics
1 answer:
atroni [7]3 years ago
7 0

Answer:

We start with y = g(x) = f(x)

First, we have a vertical stretch by a factor of 2.

A vertical strech by a factor of A will be g(x) = A*f(x)

then in this case A = 2, so we have g(x) =  2*f(x)

Now we have it shifted left by 8 units.

We know that f(x - A) shift right the graph by A units (A positive), here A = 8.

then we have: g(x) =  2*f(x - 8)

Now we want shift up 3 units, if we have y = f(x) we can shift the graph up by A units as: y = g(x) + A (for A positive)

Then we have: g(x) =  2*f(x - 8) + 3

now, our function was f(x) = Log₅(x)

then g(x) = 2*log₅(x - 8) + 3.

You might be interested in
Graph the functions on the same coordinate axis. {f(x)=−2x+1g(x)=x2−2x−3
NikAS [45]

Answer:

(2,-3) and (-2,5)

Step-by-step explanation:

Let us graph the two equations one by one.

1. f(x)=-2x+1

If we compare this equation with the slope intercept form of a line which is given as

y=mx+c

we see that m = -1 and c =1

Hence the slope of the line is -2 and the y intercept is 1. Hence one point through which it is passing is (0,1) .

Let us find another point by putting x = 1 and solving it for y

y=-2(1)+1

y=-2+1 = -1

Let us find another point by putting x = 2 and solving it for y

y=-2(2)+1

y=-4+1 = -3

Hence the another point will be (2,-3)

Let us find another point by putting x = -2 and solving it for y

y=-2(-2)+1

y=+1 = 5

Hence the another point will be (-2,5)

Now we have two points (0,1) ,(1,-1) ,  (2,-3) and (-2,5) we joint them on line to obtain our line  

2.

g(x)=y=x^2-2x-3

y=x^2-2x+1-1-3

y=(x-1)^2-4

(y+4)=(x-1)^2

It represents the parabola opening upward with vertices (1,-4)

Let us mark few coordinates so that we may graph the parabola.

i) x=0 ; y=y=(0)^2-2(0)-3=0-0-3=-3 ; (0,-3)

ii)x=-1 ; y=(-1)^2-2(-1)-3=1+2-3=0 ; (-1,0)

iii) x=2 ; y=(2)^2-2(2)-3 = 4-4-3 =-3 ;(2,-3)

iii) x=1 ; y=(1)^2-2(1)-3 = 1-2-3 =-4  ;(1,-4)

iii) x=-2 ; y=(-2)^2-2(-2)-3 = 4+4-3 =5  ;(-2,5)

Now we plot them on coordinate axis and line them to form our parabola

When we plot them we see that we have two coordinates (2,-3) and (-2,5) are common , on which our graphs are intersecting. These coordinates are solution to the two graphs.

3 0
3 years ago
2) If the sales tax rate is 6.25% in Rio Rancho, how much would the sales tax be for a pair of shoes that cost
Marianna [84]

Answer:

D

Step-by-step explanation:

4 0
3 years ago
Need help please it’s due today show work
Diano4ka-milaya [45]

Answer:

D

Step-by-step explanation:

6 0
3 years ago
If f(x)=|x+7|, find f(−12).<br><br><br> −19<br><br><br> −5<br><br><br> 5<br><br><br> 19
Slav-nsk [51]

Answer:

5

Step-by-step explanation:

insert f(-12) for f(x) and solve

f(-12)=|-12+7|

add -12 and 7

f(-12)=|-5|

absolute value makes it positive

f(-12)=5

6 0
3 years ago
Read 2 more answers
What is the square root of 225 and 226? Also what is a short cut I could use to figure this out more easily?
Reptile [31]
The square root of 255+266 is 241. I can't help you with shortcuts as I'm bad at explaining, but I'm sure there are websites that can help you.
6 0
3 years ago
Read 2 more answers
Other questions:
  • Luis counts the total number of ducks swimming on a pond each day. On Monday he counts 1 duck. On Tuesday he counts 2 ducks. On
    15·2 answers
  • Susan works as a hostess where she makes $8.75 per hour she also babysits an earns $10.00 per hour. last week she make $165.00.
    6·1 answer
  • last year, kendra was 4.5 feet tall, and she weighed 60 pounds. this year, she's 5.5 feet tall, and she weighs 70 pounds. did he
    13·1 answer
  • -[x-2]=x+2 please help
    9·1 answer
  • n ant needs to travel along a 20cm × 20cm cube to get from point A to point B. What is the shortest path he can take, and how lo
    8·1 answer
  • Help please! show your steps please​
    11·1 answer
  • PLEASE HELP ME I NEED IT FOR A TEST
    13·2 answers
  • Answer this and ill give you all my points if you answer them all.
    12·1 answer
  • \frac{7}{4} \frac{13}{2}[/tex]
    11·2 answers
  • What is the value of the expression 8/15 divided by (-0.35)
    8·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!